Chain Recurrence Rates and Topological Entropy

On the Interplay between Measurable and Topological Dynamics E. Glasner and B. Weiss

Part 1. Analogies 3 1. Poincaré recurrence vs. Birkhoff’s recurrence 3 1.1. Poincaré recurrence theorem and topological recurrence 3 1.2. The existence of Borel cross-sections 4 1.3. Recurrence sequences and Poincaré sequences 5 2. The equivalence of weak mixing and continuous spectrum 7 3. Disjointness: measure vs. topological 10 4. Mild mixing: measure vs. topological 12 5. Distal systems: to...

On the Interplay between Measurable and Topological Dynamics

Part 1. Analogies 3 1. Poincaré recurrence vs. Birkhoff’s recurrence 3 1.1. Poincaré recurrence theorem and topological recurrence 3 1.2. The existence of Borel cross-sections 4 1.3. Recurrence sequences and Poincaré sequences 5 2. The equivalence of weak mixing and continuous spectrum 7 3. Disjointness: measure vs. topological 10 4. Mild mixing: measure vs. topological 12 5. Distal systems: to...

Dynamically Deened Recurrence Dimension

In this paper, we introduce and characterize the dynamically deened recurrence dimension, a new topological invariant number, following the idea of a previous article 9], but with some modiications and improvements. We study some example of Toeplitz subshifts for which we can show that the recurrence dimension is a topologically invariant number diierent from the topological entropy.

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.

QSPR Modeling of Heat Capacity, Thermal Energy and Entropy of Aliphatic Aldehydes by using Topological Indices and MLR Method