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Documents  37B50 | enregistrements trouvés : 6

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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

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

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

Tiling billiards is a dynamical system where beams of light refract through planar tilings. It turns out that, for a regular tiling of the plane by congruent triangles, the light trajectories can be described by interval exchange transformations. I will explain this surprising correspondence, give related results, and show computer simulations of the system.

37D50 ; 37B50

Subshifts of finite type are of high interest from a computational point of view, since they can be described by a finite amount of information - a set of forbidden patterns that defines the subshift - and thus decidability and algorithmic questions can be addressed. Given an SFT $X$, the simplest question one can formulate is the following: does $X$ contain a configuration? This is the so-called domino problem, or emptiness problem: for a given finitely presented group $0$, is there an algorithm that determines if the group $G$ is tilable with a finite set of tiles? In this lecture I will start with a presentation of two different proofs of the undecidability of the domino problem on $Z^2$. Then we will discuss the case of finitely generated groups. Finally, the emptiness problem for general subshifts will be tackled. Subshifts of finite type are of high interest from a computational point of view, since they can be described by a finite amount of information - a set of forbidden patterns that defines the subshift - and thus decidability and algorithmic questions can be addressed. Given an SFT $X$, the simplest question one can formulate is the following: does $X$ contain a configuration? This is the so-called domino problem, or emptiness problem: for a given ...

68Q45 ; 03B25 ; 37B50

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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