5 papers
The Variational Principle for a Action on a Hausdorff Locally Compact Space
André Caldas, Hermano Farias
We extend the definition of topological pressure to locally compact Hausdorff spaces, and we demonstrate a "variational principle" comparing the topological and measure theoretic p…
Topological Pressure for Locally Compact Metrizable Systems
André Caldas
It is widely known that when is compact Hausdorff, and when and are continuous, \begin{equation*} P(T,f) = \sup_{\text{: Radon probability…
Entropy and Its Variational Principle for Locally Compact Metrizable Systems
André Caldas, Mauro Patrão
For a given topological dynamical system over a compact set with a metric , the "variational principle" states that \begin{equation*} \sup_μh_μ(T) = h(T) = h_d(T), \…
Entropy and Its Variational Principle for Product Type Dynamical Systems
André Caldas, Mauro Patrão
This paper has a flaw in an argument that uses the weak-* convergence of measures. The paper was replaced by "Entropy and Its Variational Principle for Locally Compact Metrizable S…
Entropy of Endomorphisms of Lie Groups
André Caldas, Mauro Patrão
We show, when is a nilpotent or reductive Lie group, that the entropy of any surjective endomorphism coincides with the entropy of its restriction to the toral component of the…