2025/11/17 by Marco Martens, Martens, Marco, Liviana Palmisano +1
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2511.12926
openalex publication_date 2025/11/17 · openalex created_date 2025/11/19 · openalex updated_date 2026/07/28
In two-dimensional unfoldings of homoclinic tangencies, the parameter space contains codimension one laminations whose leaves consist of maps with invariant non-hyperbolic Cantor sets. These Cantor sets are wild both in the sense of Hofbauer-Keller and in the sense of Newhouse, and they contain Collet-Eckmann points with dense orbits. Hence, wildness and non-uniform chaotic hyperbolicity can coexist on a single invariant set, while persisting along codimension one manifolds. In addition, each leaf of the lamination contains a map with infinitely many sinks accumulating on the Cantor set containing the Collet-Eckmann point. This surprising symbiosis of contraction and expansion may not, in fact, be pathological. Along the way, we introduce a generalized renormalization scheme for two-dimensional systems.