Topological Pressure for One-Dimensional Holomorphic Dynamical Systems

Topological Pressure for One-dimensional Holomorphic Dynamical Systems

For a class of one-dimensional holomorphic maps f of the Riemann sphere we prove that for a wide class of potentials φ the topological pressure is entirely determined by the values of φ on the repelling periodic points of f . This is a version of a classical result of Bowen for hyperbolic diffeomorphisms in the holomorphic non-uniformly hyperbolic setting.

Entropy operator for continuous dynamical systems of finite topological entropy

In this paper we introduce the concept of entropy operator for continuous systems of finite topological entropy. It is shown that it generates the Kolmogorov entropy as a special case. If $phi$ is invertible then the entropy operator is bounded with the topological entropy of $phi$ as its norm.

Topological Pressure of Nonautonomous Dynamical Systems ⋆

We define and study topological pressure for the non-autonomous discrete dynamical systems given by a sequence {fi} ∞ i=1 of continuous self-maps of a compact metric space. In this paper, we obtain the basic properties and the invariant with respect to equiconjugacy of topological pressure for the nonautonomous discrete dynamical systems.

A topological delay embedding theorem for infinite-dimensional dynamical systems

A time delay reconstruction theorem inspired by that of Takens (1981 Springer Lecture Notes in Mathematics vol 898, pp 366–81) is shown to hold for finite-dimensional subsets of infinite-dimensional spaces, thereby generalizing previous results which were valid only for subsets of finite-dimensional spaces. Let A be a subset of a Hilbert space H with upper box-counting dimension d(A) = d and ‘t...

Discrete Holomorphic Local Dynamical Systems