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Research talks

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 ...

37B10 ; 37A25 ; 68R15

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2 y

Research schools

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, ...

37B50 ; 37B10 ; 37B40

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y

Research schools

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, ...

37B50 ; 37B10 ; 37B40

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y

Research schools

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, ...

37B50 ; 37B10 ; 37B40

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V

- 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

37-06 ; 37Axx ; 37B10

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V

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

Localisation : Colloque RdC

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

37-01 ; 37D40 ; 58-06 ; 28Dxx ; 37B10

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V

- 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

37B10 ; 37B50 ; 37-06 ; 37A15 ; 37F45 ; 94B05 ; 19C99

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V

- 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

11K16 ; 11F06 ; 11A55 ; 11K50 ; 28D20 ; 37B10 ; 42A38 ; 42C40 ; 65M12 ; 93B05

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V

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

Localisation : Colloque RdC

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

37-06 ; 37Cxx ; 37B10 ; 82D25

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V

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

Contemporary mathematics , 0503

Localisation : Collection 1er étage

théorie des opérateurs # dynamique # système dynamique

46L55 ; 37BXX ; 47LXX ; 46L08 ; 46L35 ; 46H25 ; 37B10 ; 37FXX ; 16S35 ; 54H20

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V

- 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 # ...

11A67 ; 11K55 ; 15A48 ; 28A12 ; 28D05 ; 28D20 ; 32G15 ; 37Axx ; 37B05 ; 37B10 ; 37B15 ; 37D40 ; 37D45 ; 37E05 ; 30F30 ; 53D25 ; 57R30

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V

- 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 ...

05E10 ; 14F10 ; 14F42 ; 14J70 ; 17B37 ; 11F72 ; 11R39 ; 14-02 ; 14C25 ; 14D07 ; 19K35 ; 20-02 ; 20B30 ; 20C15 ; 20C33 ; 20D05 ; 20E32 ; 20F05 ; 20F12 ; 20G15 ; 20G40 ; 20H10 ; 20P05 ; 22E55 ; 30F30 ; 30F40 ; 32G15 ; 32G20 ; 32Q45 ; 32S35 ; 32S60 ; 35K05 ; 37B10 ; 37B50 ; 43A07 ; 49J45 ; 53C21 ; 57M50 ; 58A20 ; 60G70 ; 60H15 ; 60J65 ; 60J80 ; 82C28

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y

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

Contemporary mathematics , 0678

Localisation : Collection 1er étage

théorie ergodique # système dynamique # John C. Oxtoby

37A05 ; 37B05 ; 37A40 ; 37B50 ; 37B10 ; 37A30 ; 37A20 ; 01A70

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y

Research schools

An automorphism of a subshift $X$ is a self-homeomorphism of $X$ that commutes with the shift map. The study of these automorphisms started at the very beginning of the symbolic dynamics. For instance, the well known Curtis-Hedlund-Lyndon theorem asserts that each automorphism is a cellular automaton. The set of automorphisms forms a countable group that may be very complicated for mixing shift of finite type (SFT). The study of this group for low complexity subshifts has become very active in the last five years. Actually, for zero entropy subshift, this group is much more tame than in the SFT case. In a first lecture we will recall some striking property of this group for subshift of finite type. The second lecture is devoted to the description of this group for classical minimal sub shifts of zero entropy with sublinear complexity and for the family of Toeplitz subshifts. The last lecture concerns the algebraic properties of the automorphism group for subshifts with sub-exponential complexity. We will also explain why sonic group like the Baumslag-Solitar $BS(1,n)$ or $SL(d,Z), d >2$, can not embed into an automorphism group of a zero entropy subshift. An automorphism of a subshift $X$ is a self-homeomorphism of $X$ that commutes with the shift map. The study of these automorphisms started at the very beginning of the symbolic dynamics. For instance, the well known Curtis-Hedlund-Lyndon theorem asserts that each automorphism is a cellular automaton. The set of automorphisms forms a countable group that may be very complicated for mixing shift of finite type (SFT). The study of this group for ...

37B10 ; 37B50 ; 37B15 ; 68Q80

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y

Research schools

I shall discuss old and new results on amenability of groups, and more generally G-sets. This notion traces back to von Neumann in his study of the Hausdorff-Banach-Tarski paradox, and grew into one of the fundamental properties a group may / may not have -- each time with important consequences.
Lecture 1. I will present the classical notions and equivalent definitions of amenability, with emphasis on group actions and on combinatorial aspects: Means, Folner sets, random walks, and paradoxical decompositions.
Lecture 2. I will describe recent work by de la Salle et al. leading to a quite general criterion for amenability, as well as some still open problems. In particular, I will show that full topological groups of minimal Z-shifts are amenable.
Lecture 3. I will explain links between amenability and cellular automata, in particular the "Garden of Eden" properties by Moore and Myhill: there is a characterization of amenable groups in terms of whether these classical theorems still hold.
I shall discuss old and new results on amenability of groups, and more generally G-sets. This notion traces back to von Neumann in his study of the Hausdorff-Banach-Tarski paradox, and grew into one of the fundamental properties a group may / may not have -- each time with important consequences.
Lecture 1. I will present the classical notions and equivalent definitions of amenability, with emphasis on group actions and on combinatorial aspects: ...

37B15 ; 37B10 ; 43A07 ; 68Q80

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y

Research talks

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.

37B10 ; 37D40 ; 34C28 ; 37C20 ; 37C40 ; 37D35

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y

Research schools

28A80 ; 37A30 ; 37B10 ; 37E05 ; 11B85 ; 11B83 ; 68R15

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V

- 205 p.
ISBN 978-3-540-67434-4

Lecture notes in mathematics , 1732

Localisation : Collection 1er étage

système dynamique # dynamique topologique # ensemble de Julia # équivalence de Julia # ensemble de Mandelbrot # orbite # suite de Sturn # facteur invariant # fractale # famille holomorphe de systèmes dynamiques # équation fonctionnelle dans un domaine complexe

30D05 ; 54H20 ; 37B10

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V

- 252 p.
ISBN 978-3-540-62738-8

Universitext

Localisation : Ouvrage (KITC)

automorphisme # système dynamique # dynamique symbolique # conjugaison topologique # décalage de Markov # automate cellulaire

37B10 ; 37BXX ; 54H20 ; 28D20

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V

- 495 p.
ISBN 978-0-521-55124-3

Localisation : Ouvrage RdC (LIND)

système dynamique # dynamique symbolique # sous-shifts de type fini # système sofique # entropie # codage # classification des sous-shifts de type fini

37B10 ; 15A48 ; 37BXX ; 54H20 ; 94A24 ; 94B60 ; 37C30

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