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# Documents  37B10 | enregistrements trouvés : 49

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## Introduction to hierarchical tiling dynamical systems: Supertile construction methods Frank, Natalie Priebe | CIRM H

Post-edited

Research schools;Dynamical Systems and Ordinary Differential Equations;Geometry

These lectures introduce the dynamical systems approach to tilings of Euclidean space, especially quasicrystalline tilings that have been constructed using a ‘supertile method’. Because tiling dynamics parallels one-dimensional symbolic dynamics, we discuss this case as well, highlighting the differences and similarities in the methods of study and the results that can be obtained.
In the first lecture we motivate the field with the discovery of quasicrystals, which led to D. Schectman’s winning the 2011 Nobel Prize in Chemistry. Then we set up the basics of tiling dynamics, describing tiling spaces, a tiling metric, and the shift or translation actions. Shift-invariant and ergodic measures are discussed, along with fundamental topological and dynamical properties.
The second lecture brings in the supertile construction methods, including symbolic substitutions, self-similar tilings, $S$-adic systems, and fusion rules. Numerous examples are given, most of which are not the “standard” examples, and we identify many commonalities and differences between these interrelated methods of construction. Then we compare and contrast dynamical results for supertile systems, highlighting those key insights that can be adapted to all cases.
In the third lecture we investigate one of the many current tiling research areas: spectral theory. Schectman made his Nobel-prize-winning discovery using diffraction analysis, and studying the mathematical version has been quite fruitful. Spectral theory of tiling dynamical systems is also of broad interest. We describe how these types of spectral analysis are carried out, give examples, and discuss what is known and unknown about the relationship between dynamical and diffraction analysis. Special attention is paid to the “point spectrum”, which is related to eigenfunctions and also to the bright spots that appear on diffraction images.
These lectures introduce the dynamical systems approach to tilings of Euclidean space, especially quasicrystalline tilings that have been constructed using a ‘supertile method’. Because tiling dynamics parallels one-dimensional symbolic dynamics, we discuss this case as well, highlighting the differences and similarities in the methods of study and the results that can be obtained.
In the first lecture we motivate the field with the discovery of ...

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## Ergodic measures for subshifts with eventually constant growth Fickenscher, Jon | CIRM H

Post-edited

Research talks;Combinatorics;Computer Science;Dynamical Systems and Ordinary Differential Equations

We will consider (sub)shifts with complexity such that the difference from $n$ to $n+1$ is constant for all large $n$. The shifts that arise naturally from interval exchange transformations belong to this class. An interval exchange transformation on d intervals has at most $d/2$ ergodic probability measures. We look to establish the correct bound for shifts with constant complexity growth. To this end, we give our current bound and discuss further improvements when more assumptions are allowed. This is ongoing work with Michael Damron. We will consider (sub)shifts with complexity such that the difference from $n$ to $n+1$ is constant for all large $n$. The shifts that arise naturally from interval exchange transformations belong to this class. An interval exchange transformation on d intervals has at most $d/2$ ergodic probability measures. We look to establish the correct bound for shifts with constant complexity growth. To this end, we give our current bound and discuss ...

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## Entropy and mixing for multidimensional shifts of finite type - Lecture 3 Pavlov, Ronnie | CIRM H

Post-edited

Research schools;Dynamical Systems and Ordinary Differential Equations

I will speak about multidimensional shifts of finite type and their measures of maximal entropy. In particular, I will present results about computability of topological entropy for SFTs and measure-theoretic entropy. I'll focus on various mixing hypotheses, both topological and measure-theoretic, which imply different rates of computability for these objects, and give applications to various systems, including the hard square model, k-coloring, and iceberg model. I will speak about multidimensional shifts of finite type and their measures of maximal entropy. In particular, I will present results about computability of topological entropy for SFTs and measure-theoretic entropy. I'll focus on various mixing hypotheses, both topological and measure-theoretic, which imply different rates of computability for these objects, and give applications to various systems, including the hard square model, k-coloring, ...

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## Entropy and mixing for multidimensional shifts of finite type - Lecture 2 Pavlov, Ronnie | CIRM H

Post-edited

Research schools;Dynamical Systems and Ordinary Differential Equations

I will speak about multidimensional shifts of finite type and their measures of maximal entropy. In particular, I will present results about computability of topological entropy for SFTs and measure-theoretic entropy. I'll focus on various mixing hypotheses, both topological and measure-theoretic, which imply different rates of computability for these objects, and give applications to various systems, including the hard square model, k-coloring, and iceberg model. I will speak about multidimensional shifts of finite type and their measures of maximal entropy. In particular, I will present results about computability of topological entropy for SFTs and measure-theoretic entropy. I'll focus on various mixing hypotheses, both topological and measure-theoretic, which imply different rates of computability for these objects, and give applications to various systems, including the hard square model, k-coloring, ...

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## Entropy and mixing for multidimensional shifts of finite type - Lecture 1 Pavlov, Ronnie | CIRM H

Post-edited

Research schools;Dynamical Systems and Ordinary Differential Equations

I will speak about multidimensional shifts of finite type and their measures of maximal entropy. In particular, I will present results about computability of topological entropy for SFTs and measure-theoretic entropy. I'll focus on various mixing hypotheses, both topological and measure-theoretic, which imply different rates of computability for these objects, and give applications to various systems, including the hard square model, k-coloring, and iceberg model. I will speak about multidimensional shifts of finite type and their measures of maximal entropy. In particular, I will present results about computability of topological entropy for SFTs and measure-theoretic entropy. I'll focus on various mixing hypotheses, both topological and measure-theoretic, which imply different rates of computability for these objects, and give applications to various systems, including the hard square model, k-coloring, ...

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## Topics in symbolic dynamics and applications :courses given at the CIMPA-UNESCO summer school on ...#January 6-24 Blanchard, F. ; Maass, A. ; Nogueira, A. | Cambridge University Press 2000

Congrès

- 245 p.
ISBN 978-0-521-79660-6

London mathematical society lecture note series , 0279

Localisation : Collection 1er étage

dynamique symbolique # théorie ergodique # dynamique topologique # sous-groupe de Markov # automate fini # entropie topologique # classification topologique # problème diophantien # loi asymptotique # théorie combinatoire de Ramsey

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## Symbolic dynamics and its applications :AMS short course#Janv. 4-5 Williams, Susan G. | American Mathematical Society 2004

Congrès

- 156 p.
ISBN 978-0-8218-2816-8

Proceedings of symposia in applied mathematics , 0060

Localisation : Collection 1er étage

dynamique symbolique # pavage # code correcteur d'erreur # code linéaire # dynamique complexe # groupe de Steinberg

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## Séminaire Bourbaki. Vol. 2012/2013: exposés 1059-1073 | Société Mathématique de France 2014

Congrès

- x; 520 p.
ISBN 978-2-85629-785-8

Astérisque , 0361

Localisation : Périodique 1er étage

actions commensurantes # algèbre de Steenrod # algèbres de Lie semi-simple # bases canoniques # biparti # caractère # carte # cartes de mots # catégorification # classification # cohomologie étale # cohomologie galoisienne # cohomologie motivique # commutateurs # complexe des courbes # conjecture de Baum-Connes # conjecture de Bloch-Kato # conjecture de Hodge # conjecture d'Ore # conjecture de Thompson # constantes de Siegel-Veech # corps d'Okounkov # courbure # cycles algébriques # déterminant du laplacien diagramme de Young # différentielles holomorphes # dimension d'Iitaka # distance de Wasserstein # dynamique symbolique # échanges d'intervalles # ÉDP d'évolution # ÉDP stochastiques # endoscopie tordue # équations F-KPP # espace de modules de différentielles quadratiques # espaces métriques mesurés # exposants de Lyapunov # extrêmes # flot de la chaleur # flot géodésique de Teichmüller # flots de gradient # fonction de Hilbert # fonctorialité # formes automorphes de carré intégrable # graphe expanseur # groupe hyperbolique # groupes approximativement finis # groupes classiques # groupes élémentairement moyennables # groupes kleiniens # groupes moyennables # groupes pleins-topologiques # groupes quantiques # homéomorphismes minimaux # hyperbolicité au sens de Kobayashi # inégalités de Morse holomorphes # KK-théorie # K-théorie de Milnor # laminations terminales # mouvement brownien branchant # odomètres # partition # polynôme de Kerov propriété (T) # renormalisation # sous-décalages topologiques # surfaces plates # symétriseur de Young # théorie homotopique des schémas # trajectoires rugueuses # unicellulaire # variations de structure de Hodge actions commensurantes # algèbre de Steenrod # algèbres de Lie semi-simple # bases canoniques # biparti # caractère # carte # cartes de mots # catégorification # classification # cohomologie étale # cohomologie galoisienne # cohomologie motivique # commutateurs # complexe des courbes # conjecture de Baum-Connes # conjecture de Bloch-Kato # conjecture de Hodge # conjecture d'Ore # conjecture de Thompson # constantes de Siegel-Veech # corps ...

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## Operator Structures and Dynamical Systems :Satellite Conference of the Fifth European Congress of Mathematics Leiden # July, 21-25, 2008, Jeu, Marcel de ; Silvestrov, Sergei ; Skau, Christian ; Tomiyama, Jun | American Mathematical Society 2009

Congrès

- X-317 p.
ISBN 978-0-8218-4747-3

Contemporary mathematics , 0503

Localisation : Collection 1er étage

théorie des opérateurs # dynamique # système dynamique

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## European women in mathematics :proceedings of the 11th conference of EWM Dajani, Karma ; Von Reis, J. | Stichting Mathematisch Centrum 2005

Congrès

- 120 p.
ISBN 978-90-6196-527-5

CWI tract , 0135

Localisation : Collection 1er étage

femmes et mathématiques # nombre normal # structure de groupe modulaire # fraction continue # théorie métrique des fractions continues # entropie # dynamique symbolique # transformation de Fourier # ondelettes # stabilité des méthodes numériques # convergence des méthodes numériques # convergence

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## Ergodic theory, symbolic dynamics and hyperbolic spaces :lectures given at the workshop on ... held at the International Centre for Theoretical Physics#April 17-28 Bedford, Tim ; Keane, Michael ; Series, Caroline | Oxford University Press 1992

Congrès

- 369 p.
ISBN 978-0-19-859685-1

Localisation : Colloque 1er étage (TRIE)

théorie ergodique # géométrie hyperbolique # dynamique symbolique # fonction zeta # groupe fuchsien # géodésique # espace hyperbolique

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## Ergodic theory, dynamical systems, and the continuing influence of John C. Oxtoby.Oxtoby centennial conferenceBryn Mawr # October 30-31, 2010.Williams ergodic theory conferenceWilliamstown # July 27-29, 2012.AMS special session on ergodic theory and symbolic dynamicsBaltimore # January 17-18, 2014 Auslander, Joseph ; Johnson, Aimee ; Silva, Cesar E. | American Mathematical Society 2016

Congrès

- xvi; 316 p.
ISBN 978-1-4704-2299-8

Contemporary mathematics , 0678

Localisation : Collection 1er étage

théorie ergodique # système dynamique # John C. Oxtoby

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## Ecole de théorie ergodiqueMarseille # avril 2006 Lacroix, Yves ; Liardet, Pierre ; Thouvenot, Jean-Paul | Société Mathématique de France 2010

Congrès

- xxii; 266 p.
ISBN 978-2-85629-312-6

Séminaires et congrès , 0020

Localisation : Collection 1er étage

bêta-numération # application premier retour # applications d'intervalles # applications fer à cheval # applications monotones par morceaux # attracteurs # auto-couplage # automate cellulaire # cobord # convolutions de Bernoulli # décalages markoviens fortement positivement récurrents # développements glouton et paresseux # diagramme de Markov # dimension de Hausdorff # dynamique symbolique # dynamiques directionnelles # échelles de numération # entropie # feuilletage linéaire # flot géodésique # géométrie fractale # invariants par tricotage # mélange faible # mesure d'Erdös # mesure invariante # mesure invariante absolument continue # mesures de Gibbs et faiblement gibbsiennes # mesures d'entropie maximale # métrique euclidienne # nombre d'or # odomètre # orbites périodiques # partition markovienne # pistage # principe variationnel # problème de rigidité # rang faible # section transverse # sous-décalage de Toeplitz # surface plate # surface pointée # système dynamique # systèmes dynamiques en topologie et en combinatoire # systèmes dynamiques minimaux # systèmes dynamiques symboliques # théorie des suites de tricotage # théorie ergodique # transformation de rang un # zêta fonction de Artin-Mazur bêta-numération # application premier retour # applications d'intervalles # applications fer à cheval # applications monotones par morceaux # attracteurs # auto-couplage # automate cellulaire # cobord # convolutions de Bernoulli # décalages markoviens fortement positivement récurrents # développements glouton et paresseux # diagramme de Markov # dimension de Hausdorff # dynamique symbolique # dynamiques directionnelles # échelles de numération # ...

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## Dynamical systems from crystal to chaos :proceedings of the conference in honor of Gerard Rauzy on his 60th birthday#July 6-10 Gambaudo, Jean-Marc ; Tardieu, Hubert Av.-Prop. ; Tisseur, P. ; Vaienti, S. | World Scientific 2000

Congrès

- 306 p.
ISBN 978-981-02-4217-6

Localisation : Colloque 1er étage (MARS)

système dynamique # système dynamique discret # dynamique symbolique # dynamique statistique # réseau neuronal # billard # cristal # chaos

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## Yet another characterization of the Pisot conjecture Mercat, Paul | CIRM H

Multi angle

Research talks;Computer Science;Dynamical Systems and Ordinary Differential Equations;Number Theory

In the way of Arnoux-Ito, we give a general geometric criterion for a subshift to be measurably conjugated to a domain exchange and to a translation on a torus. For a subshift coming from an unit Pisot irreducible substitution, we will see that it becomes a simple topological criterion. More precisely, we define a topology on $\mathbb{Z}^d$ for which the subshift has pure discrete spectrum if and only if there exists a domain of the domain exchange on the discrete line that has non-empty interior. We will see how we can compute exactly such interior using regular languages. This gives a way to decide the Pisot conjecture for any example of unit Pisot irreducible substitution.
Joint work with Shigeki Akiyama.
In the way of Arnoux-Ito, we give a general geometric criterion for a subshift to be measurably conjugated to a domain exchange and to a translation on a torus. For a subshift coming from an unit Pisot irreducible substitution, we will see that it becomes a simple topological criterion. More precisely, we define a topology on $\mathbb{Z}^d$ for which the subshift has pure discrete spectrum if and only if there exists a domain of the domain ...

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## Symbolic bounded remainder sets Berthé, Valérie | CIRM H

Multi angle

Research talks

Discrepancy is a measure of equidistribution for sequences of points. We consider here discrepancy in the setting of symbolic dynamics and we discuss the existence of bounded remainder sets for some families of zero entropy subshifts, from a topological dynamics viewpoint. A bounded remainder set is a set which yields bounded discrepancy, that is, the number of times it is visited differs by the expected time only by a constant. Bounded discrepancy provides particularly strong convergence properties of ergodic sums. It is also closely related to the notions of balance in word combinatorics. Discrepancy is a measure of equidistribution for sequences of points. We consider here discrepancy in the setting of symbolic dynamics and we discuss the existence of bounded remainder sets for some families of zero entropy subshifts, from a topological dynamics viewpoint. A bounded remainder set is a set which yields bounded discrepancy, that is, the number of times it is visited differs by the expected time only by a constant. Bounded ...

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## Generic properties of the geodesic flow in nonpositive curvature Coudène, Yves | CIRM H

Multi angle

Research talks;Dynamical Systems and Ordinary Differential Equations

I will survey recent results on the generic properties of probability measures invariant by the geodesic flow defined on a nonpositively curved manifold. Such a flow is one of the early example of a non-uniformly hyperbolic system. I will talk about ergodicity and mixing both in the compact and noncompact setting, and ask some questions about the associated frame flow, which is partially hyperbolic.

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## Exemple d'Arnoux-Yoccoz, fractal de Rauzy, problème de Novikov : brins d'une guirlande éternelle Hubert, Pascal | CIRM H

Multi angle

Research schools;Analysis and its Applications;Combinatorics;Dynamical Systems and Ordinary Differential Equations;Number Theory

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## Dimension groups and recurrence for tree subshifts Berthé, Valérie | CIRM H

Multi angle

Research talks;Computer Science;Dynamical Systems and Ordinary Differential Equations

Dimension groups are invariants of orbital equivalence. We show in this lecture how to compute the dimension group of tree subshifts. Tree subshifts are defined in terms of extension graphs that describe the left and right extensions of factors of their languages: the extension graphs are trees. This class of subshifts includes classical families such as Sturmian, Arnoux-Rauzy subshifts, or else, codings of interval exchanges. We rely on return word properties for tree subshifts: every finite word in the language of a tree word admits exactly d return words, where d is the cardinality of the alphabet.
This is joint work with P. Cecchi, F. Dolce, F. Durand, J. Leroy, D. Perrin, S. Petite.
Dimension groups are invariants of orbital equivalence. We show in this lecture how to compute the dimension group of tree subshifts. Tree subshifts are defined in terms of extension graphs that describe the left and right extensions of factors of their languages: the extension graphs are trees. This class of subshifts includes classical families such as Sturmian, Arnoux-Rauzy subshifts, or else, codings of interval exchanges. We rely on return ...

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## Beyond Bowen specification property - lecture 3 Climenhaga, Vaughn | CIRM H

Multi angle

Research schools

Rufus Bowen introduced the specification property for uniformly hyperbolic dynamical systems and used it to establish uniqueness of equilibrium states, including the measure of maximal entropy. After reviewing Bowen's argument, we will present our recent work on extending Bowen's approach to non-uniformly hyperbolic systems. We will describe the general result, which makes precise the notion of "entropy (orpressure) of obstructions to specification" using a decomposition of the space of finite-length orbit segments, and then survey various applications, including factors of beta-shifts, derived-from-Anosov diffeomorphisms, and geodesic flows in non-positive curvature and beyond. Rufus Bowen introduced the specification property for uniformly hyperbolic dynamical systems and used it to establish uniqueness of equilibrium states, including the measure of maximal entropy. After reviewing Bowen's argument, we will present our recent work on extending Bowen's approach to non-uniformly hyperbolic systems. We will describe the general result, which makes precise the notion of "entropy (orpressure) of obstructions to s...

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