A chaotic function with zero topological entropy having a non-perfect attractor
A generalisation of Mahler measure and its application in algebraic dynamical systems
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
A local approach to -entropy
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
A Mixing T for which T - T... Is Bernoulli.
A non-ergodic version of Rudolph's theorem
A note on the approximation by continued fractions under an extra condition.
A note on the relation between asymptotic rates of a flow under a function and its basis-automorphism
A relation between dimension of the harmonic measure, entropy and drift for a random walk on a hyperbolic space.
A representation theorem for perfect partitions of -actions with finite entropy
A Short Proof of a Theorem of Ruelle.
A Skew-Product Which is Bernoulli.
A weighted ergodic maximal equality for nonsingular semiflows
A weighted ergodic maximal equality is proved for a conservative and ergodic semiflow of nonsingular automorphisms.
Abelian groups of zero adjoint entropy
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
Action minimizing invariant measures for positive definite Lagrangian systems.
Almost-Topological Representation Theorems for Dynamical Systems.
An analogue of the Variational Principle for group and pseudogroup actions
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.