A chaotic function with zero topological entropy having a non-perfect attractor
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A generalisation of Mahler measure and its application in algebraic dynamical systems
Manfred Einsiedler (1999)
Acta Arithmetica
We prove a generalisation of the entropy formula for certain algebraic -actions given in [2] and [4]. This formula expresses the entropy as the logarithm of the Mahler measure of a Laurent polynomial in d variables with integral coefficients. We replace the rational integers by the integers in a number field and examine the entropy of the corresponding dynamical system.
A group automorphism is a factor of a direct product of a zero entropy automorphism and a Bernoulli automorphism
Nobuo Aoki (1981)
Fundamenta Mathematicae
A local approach to -entropy
Mehdi Rahimi (2015)
Kybernetika
In this paper, a local approach to the concept of -entropy is presented. Applying the Choquet‘s representation Theorem, the introduced concept is stated in terms of -entropy.
A local structure of stationary perfectly noiseless codes between stationary non-ergodic sources. II. Applications
Štefan Šujan (1982)
Kybernetika
A Mixing T for which T - T... Is Bernoulli.
Paul C. Shields, Robert M. Burton (1983)
Monatshefte für Mathematik
A non-ergodic version of Rudolph's theorem
Miroslav Krutina (1990)
Kybernetika
A note on the approximation by continued fractions under an extra condition.
Dajani, Karma, Kraaikamp, Cor (1998)
The New York Journal of Mathematics [electronic only]
A note on the relation between asymptotic rates of a flow under a function and its basis-automorphism
Miroslav Krutina (1989)
Commentationes Mathematicae Universitatis Carolinae
A relation between dimension of the harmonic measure, entropy and drift for a random walk on a hyperbolic space.
Le Prince, Vincent (2008)
Electronic Communications in Probability [electronic only]
A representation theorem for perfect partitions of -actions with finite entropy
B. Kamiński (1988)
Colloquium Mathematicae
A Short Proof of a Theorem of Ruelle.
Manfred Denker, Christoph Seck (1989)
Monatshefte für Mathematik
A Skew-Product Which is Bernoulli.
Paul C. Shields, Robert Burton (1978/1979)
Monatshefte für Mathematik
A weighted ergodic maximal equality for nonsingular semiflows
Lasha Ephremidze, Ryotaro Sato (2005)
Colloquium Mathematicae
A weighted ergodic maximal equality is proved for a conservative and ergodic semiflow of nonsingular automorphisms.
Abelian groups of zero adjoint entropy
L. Salce, P. Zanardo (2010)
Colloquium Mathematicae
The notion of adjoint entropy for endomorphisms of an Abelian group is somehow dual to that of algebraic entropy. The Abelian groups of zero adjoint entropy, i.e. ones whose endomorphisms all have zero adjoint entropy, are investigated. Torsion groups and cotorsion groups satisfying this condition are characterized. It is shown that many classes of torsionfree groups contain groups of either zero or infinite adjoint entropy. In particular, no characterization of torsionfree groups of zero adjoint...
Absolutely continuous measures for certain maps of an interval
Michal Misiurewicz (1981)
Publications Mathématiques de l'IHÉS
Action minimizing invariant measures for positive definite Lagrangian systems.
John N. Mather (1991)
Mathematische Zeitschrift
Almost-Topological Representation Theorems for Dynamical Systems.
Manfred Denker (1979)
Monatshefte für Mathematik
An analogue of the Variational Principle for group and pseudogroup actions
Andrzej Biś (2013)
Annales de l’institut Fourier
We generalize to the case of finitely generated groups of homeomorphisms the notion of a local measure entropy introduced by Brin and Katok [7] for a single map. We apply the theory of dimensional type characteristics of a dynamical system elaborated by Pesin [25] to obtain a relationship between the topological entropy of a pseudogroup and a group of homeomorphisms of a metric space, defined by Ghys, Langevin and Walczak in [12], and its local measure entropies. We prove an analogue of the Variational...
An answer to a question by J. Milnor.
Ya. G. Sinai (1985)
Commentarii mathematici Helvetici
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