Symmetric homoclinic tangles in reversible dynamical systems have positive topological entropy

2022/07/21 by Homburg, Ale Jan, Lamb, Jeroen, Turaev, Dmitry
#34C37 #37B40 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2207.10624

Abstract

We consider reversible vector fields in ℝ²ⁿ such that the set of fixed points of the involutory reversing symmetry is n-dimensional. Let such system have a smooth one-parameter family of symmetric periodic orbits which is of saddle type in normal directions. We establish that topological entropy is positive when the stable and unstable manifolds of this family of periodic orbits have a strongly-transverse intersection.

Related

• Positive topological entropy and ℓ₁
• A new measure of instability and topological entropy of area-preserving\n twist diffeomorphisms
• Dynamics forced by surface trellises
• A generalized pseudo-rotation with positive topological entropy
• Positive topological entropy for the Standard Map