2023/12/27 by Sebastián Ramírez, Ramírez, Sebastián, Kendry J. Vivas +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2312.16742
openalex publication_date 2023/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we prove that the homotopy class of non-homothety linear endomorphisms on \mathbbT2 with determinant greater than 2 contains a C1 open set of non-uniformly hyperbolic endomorphisms. Furthermore, we prove that the homotopy class of non-hyperbolic elements (having either 1 or -1 as an eigenvalue) whose degree is large enough contains non-uniformly hyperbolic endomorphisms that are also C2 stably ergodic. These results provide partial answers to certain questions posed in arXiv:2206.08295v2