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Research School;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, ...
37B50 ; 37B10 ; 37B40
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Research School;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, ...
37B50 ; 37B10 ; 37B40
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Research School;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, ...
37B50 ; 37B10 ; 37B40
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Research talks;Dynamical Systems and Ordinary Differential Equations
Several recent papers on surface dynamics have used transverse foliations and maximal isotopies for homeomorphisms isotopic to the identity as a main tool in their work. In this mini-course we will introduce the basic concepts behind this tool and show a new way o deriving useful dynamical information by means of a forcing procedure. The applications involve ways of obtaining existence of non-contractible periodic points with consequences for rotation sets of toral homeomorphisms, exponential growth of periodic orbits and estimates on topological entropy of maps.
Several recent papers on surface dynamics have used transverse foliations and maximal isotopies for homeomorphisms isotopic to the identity as a main tool in their work. In this mini-course we will introduce the basic concepts behind this tool and show a new way o deriving useful dynamical information by means of a forcing procedure. The applications involve ways of obtaining existence of non-contractible periodic points with consequences for ...
37E30 ; 37E45 ; 37B40
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Research School;Analysis and its Applications;Dynamical Systems and Ordinary Differential Equations
We will discuss an approach to the statistical properties of two-dimensional dispersive billiards (mostly discrete-time) using transfer operators acting on anisotropic Banach spaces of distributions. The focus of this part will be our recent work with Mark Demers on the measure of maximal entropy but we will also survey previous results by Demers, Zhang, Liverani, etc on the SRB measure.
37D50 ; 37C30 ; 37B40
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Research School;Analysis and its Applications;Dynamical Systems and Ordinary Differential Equations
We will discuss an approach to the statistical properties of two-dimensional dispersive billiards (mostly discrete-time) using transfer operators acting on anisotropic Banach spaces of distributions. The focus of this part will be our recent work with Mark Demers on the measure of maximal entropy but we will also survey previous results by Demers, Zhang, Liverani, etc on the SRB measure.
37D50 ; 37C30 ; 37B40
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Research School;Analysis and its Applications;Dynamical Systems and Ordinary Differential Equations
We will discuss an approach to the statistical properties of two-dimensional dispersive billiards (mostly discrete-time) using transfer operators acting on anisotropic Banach spaces of distributions. The focus of this part will be our recent work with Mark Demers on the measure of maximal entropy but we will also survey previous results by Demers, Zhang, Liverani, etc on the SRB measure.
37D50 ; 37C30 ; 37B40
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Research School;Dynamical Systems and Ordinary Differential Equations
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...
37D35 ; 37B10 ; 37B40
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Research School;Dynamical Systems and Ordinary Differential Equations
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...
37D35 ; 37B10 ; 37B40
... Lire [+]
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Research School;Dynamical Systems and Ordinary Differential Equations
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...
37D35 ; 37B10 ; 37B40
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Research School;Dynamical Systems and Ordinary Differential Equations
In this talk, we will discuss various growth rates associated to Anosov flows and their covers. The topological entropy of an Anosov flow on a compact manifold is realised as the exponential growth rate of its periodic orbits. If we pass to a regular cover of the manifold then we can consider a corresponding growth rate for the lifted flow. This growth is bounded above by the topological entropy but if the cover is infinite then the growth rate may be strictly smaller. For abelian covers, this phenomenon admits a precise description in terms of a variational principle. More recent work, joint with Rhiannon Dougall, considers more general infinite covers.
In this talk, we will discuss various growth rates associated to Anosov flows and their covers. The topological entropy of an Anosov flow on a compact manifold is realised as the exponential growth rate of its periodic orbits. If we pass to a regular cover of the manifold then we can consider a corresponding growth rate for the lifted flow. This growth is bounded above by the topological entropy but if the cover is infinite then the growth rate ...
37D20 ; 37D35 ; 37D40 ; 37B40
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- 58 p.
ISBN 978-0-8218-2707-9
Memoirs of the american mathematical society , 0723
Localisation : Collection 1er étage
entropie topologique # dynamique combinatoire
37E15 ; 37B40
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- 61 p.
ISBN
Bonner mathematische schriften , 0328
Localisation : Publication 1er étage
système dynamique # entropie topologique positive # billard # billard convexe # plan hyperbolique # anneau non concentrique # analyse locale
37B40 ; 37D50 ; 37C35 ; 37C27 ; 37B10
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- 211 p.
ISBN 978-1-85233-125-2
Universitext
Localisation : Ouvrage RdC (EVER)
géométrie algébrique # mesure # système dynamique différentiable # courbe elliptique # entropie # arithmétique # mesure de Mordell
11G50 ; 11C08 ; 11G07 ; 37A45 ; 37B40 ; 37C30 ; 54H20
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- 189 p.
ISBN 978-3-540-22908-7
Universitext
Localisation : Ouvrage RdC (JOST)
système dynamique # indice de Conley # invariant topologique # entropie # théorie de Morse-Conley # exposent de Lyapunov # automate # cellulaire # réseau booléen
37B30 ; 37B40 ; 37C15 ; 37C20 ; 37G20 ; 37G35 ; 37D99
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- x; 243 p.
ISBN 978-2-85629-313-3
Panoramas et synthèses , 0032
Localisation : Collection 1er étage
Approximation diophantienne # arbres aléatoires # cascade multiplicative # chaos multiplicatif # chaîne de Markov # dimension de boîte # dimension de Hausdorff # dimension de packing # fonction multifractale # formalisme multifractal # fractals # fragmentation aléatoire # martingales # mesure multifractale # mesures # processus de branchement # produits de Riesz # recouvrements # régularité ponctuelle # spectre multifractal # systèmes dynamiques # ubiquité
Approximation diophantienne # arbres aléatoires # cascade multiplicative # chaos multiplicatif # chaîne de Markov # dimension de boîte # dimension de Hausdorff # dimension de packing # fonction multifractale # formalisme multifractal # fractals # fragmentation aléatoire # martingales # mesure multifractale # mesures # processus de branchement # produits de Riesz # recouvrements # régularité ponctuelle # spectre multifractal # systèmes dynamiques ...
11J83 ; 11K06 ; 26A15 ; 26A30 ; 28A78 ; 28A80 ; 37B40 ; 43A25 ; 60G18 ; 60J80
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- vi; 198 p.
ISBN 978-2-7598-0760-4
Savoirs actuels
Localisation : Enseignement RdC (COUD)
théorie ergodique # systèmes dynamiques # mélange # entropie # isomorphisme # décomposition ergodique dans les espaces de Lebesgue # non-errance # transitivité # mélange topologique # conjugaison # linéarisation
37-XX ; 37Axx ; 37A35 ; 37B40
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- xv; 498 p.
ISBN 978-3-11-034073-0
De Gruyter studies in mathematics , 0059
Localisation : Ouvrage RdC (VRIE)
dynamique topologique # point périodique # invariant # transitivité # conjugué # graphe de Markov # récurrence # espace de décalage # partition topologique # fer à cheval # espace de Cantor
37-01 ; 54H20 ; 37B10 ; 37B20 ; 37B25 ; 37B40 ; 37D45 ; 37E05
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