Page 1 Next

Displaying 1 – 20 of 141

Showing per page

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 d -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 local approach to g -entropy

Mehdi Rahimi (2015)


In this paper, a local approach to the concept of g -entropy is presented. Applying the Choquet‘s representation Theorem, the introduced concept is stated in terms of g -entropy.

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...

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...

Currently displaying 1 – 20 of 141

Page 1 Next