Topological entropy of a Lie group automorphism
Victor Ayala, Adriano Da Silva, Heriberto Rom\'an-Flores

TL;DR
This paper investigates the topological entropy of automorphisms on certain connected Lie groups, revealing that entropy is contained within the toral component of the unstable subgroup in the radical.
Contribution
It establishes a relation between topological entropy and the structure of Lie groups with invariant Levi subgroups, extending understanding of entropy in this context.
Findings
Entropy is contained in the toral component of the unstable subgroup
Main results apply to finite semisimple center Lie groups with invariant Levi subgroups
Specialized results for particular Lie group structures
Abstract
Let {\phi} be an automorphism on a connected Lie group G. Through several G-subgroups associated to the dynamics of {\phi} we analyze their topological entropy. Assume that G belongs to the class of finite semisimple center Lie groups which admits a {\phi} invariant Levi subgroup. Then we prove that the topological entropy information of {\phi} is contained in the toral component of the unstable subgroup of {\phi} in the radical of G. We specialize the main result in a couple of interesting situations.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Topics in Algebra · Advanced Differential Equations and Dynamical Systems
