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Tail fields generated by symbol counts in measure-preserving systems

Karl Petersen, Jean-Paul Thouvenot (2004)

Colloquium Mathematicae

A finite-state stationary process is called (one- or two-sided) super-K if its (one- or two-sided) super-tail field-generated by keeping track of (initial or central) symbol counts as well as of arbitrarily remote names-is trivial. We prove that for every process (α,T) which has a direct Bernoulli factor there is a generating partition β whose one-sided super-tail equals the usual one-sided tail of β. Consequently, every K-process with a direct Bernoulli factor has a one-sided super-K generator....

The entropy conjecture for diffeomorphisms away from tangencies

Gang Liao, Marcelo Viana, Jiagang Yang (2013)

Journal of the European Mathematical Society

We prove that every C 1 diffeomorphism away from homoclinic tangencies is entropy expansive, with locally uniform expansivity constant. Consequently, such diffeomorphisms satisfy Shub’s entropy conjecture: the entropy is bounded from below by the spectral radius in homology. Moreover, they admit principal symbolic extensions, and the topological entropy and metrical entropy vary continuously with the map. In contrast, generic diffeomorphisms with persistent tangencies are not entropy expansive.

The Language of Caring: Quantitating Medical Practice Patterns using Symbolic Dynamics

J. Paladino, A. M. Kaynar, P. S. Crooke, J. R. Hotchkiss (2010)

Mathematical Modelling of Natural Phenomena

Real-world medical decisions rarely involve binary Ðsole condition present or absent- patterns of patient pathophysiology. Similarly, provider interventions are rarely unitary in nature: the clinician often undertakes multiple interventions simultaneously. Conventional approaches towards complex physiologic derangements and their associated management focus on the frequencies of joint appearances, treating the individual derangements of physiology...

The nonexistence of universal metric flows

Stefan Geschke (2018)

Commentationes Mathematicae Universitatis Carolinae

We consider dynamical systems of the form ( X , f ) where X is a compact metric space and f : X → X is either a continuous map or a homeomorphism and provide a new proof that there is no universal metric dynamical system of this kind. The same is true for metric minimal dynamical systems and for metric abstract ω -limit sets, answering a question by Will Brian.

The number of binary rotation words

A. Frid, D. Jamet (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We consider binary rotation words generated by partitions of the unit circle to two intervals and give a precise formula for the number of such words of length n. We also give the precise asymptotics for it, which happens to be Θ(n4). The result continues the line initiated by the formula for the number of all Sturmian words obtained by Lipatov [Problemy Kibernet. 39 (1982) 67–84], then independently by Mignosi [Theoret. Comput. Sci. 82 (1991) 71–84], and others.

The universal minimal system for the group of homeomorphisms of the Cantor set

E. Glasner, B. Weiss (2003)

Fundamenta Mathematicae

Each topological group G admits a unique universal minimal dynamical system (M(G),G). For a locally compact noncompact group this is a nonmetrizable system with a rich structure, on which G acts effectively. However there are topological groups for which M(G) is the trivial one-point system (extremely amenable groups), as well as topological groups G for which M(G) is a metrizable space and for which one has an explicit description. We show that for the topological group G = Homeo(E) of self-homeomorphisms...

Three complexity functions

Sébastien Ferenczi, Pascal Hubert (2012)

RAIRO - Theoretical Informatics and Applications

For an extensive range of infinite words, and the associated symbolic dynamical systems, we compute, together with the usual language complexity function counting the finite words, the minimal and maximal complexity functions we get by replacing finite words by finite patterns, or words with holes.

Three complexity functions

Sébastien Ferenczi, Pascal Hubert (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

For an extensive range of infinite words, and the associated symbolic dynamical systems, we compute, together with the usual language complexity function counting the finite words, the minimal and maximal complexity functions we get by replacing finite words by finite patterns, or words with holes.

Three complexity functions

Sébastien Ferenczi, Pascal Hubert (2012)

RAIRO - Theoretical Informatics and Applications

For an extensive range of infinite words, and the associated symbolic dynamical systems, we compute, together with the usual language complexity function counting the finite words, the minimal and maximal complexity functions we get by replacing finite words by finite patterns, or words with holes.

Time weighted entropies

Jörg Schmeling (2000)

Colloquium Mathematicae

For invertible transformations we introduce various notions of topological entropy. For compact invariant sets these notions are all the same and equal the usual topological entropy. We show that for non-invariant sets these notions are different. They can be used to detect the direction in time in which the system evolves to highest complexity.

Tree algebra of sofic tree languages

Nathalie Aubrun, Marie-Pierre Béal (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We consider the languages of finite trees called tree-shift languages which are factorial extensible tree languages. These languages are sets of factors of subshifts of infinite trees. We give effective syntactic characterizations of two classes of regular tree-shift languages: the finite type tree languages and the tree languages which are almost of finite type. Each class corresponds to a class of subshifts of trees which is invariant by conjugacy. For this goal, we define a tree algebra which...

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