3 papers
math.DS2026
Robust heterodimensional cycles in two-parameter unfolding of homoclinic tangencies
Dongchen Li, Xiaolong Li, Katsutoshi Shinohara +1
We establish a necessary and sufficient condition for the birth of heterodimensional cycles from a generic homoclinic tangency to a hyperbolic periodic orbit. We prove for ($…
math.DS2025
Smooth Persistence of Attractors for Set-Valued Dynamical Systems: A Boundary Map Approach
K. Kourliouros, J. S. W. Lamb, M. Rasmussen +3
We study the problem of persistence of attractors with smooth boundary for a class of set-valued dynamical systems that naturally arise in the context of random and control dynamic…
math.DS2025
Symmetric homoclinic tangles in reversible dynamical systems have positive topological entropy
Ale Jan Homburg, Jeroen Lamb, Dmitry Turaev
We consider reversible vector fields in such that the set of fixed points of the involutory reversing symmetry is -dimensional. Let such system have a smooth o…