2016/06/23 by Azam Ehsani, Ehsani, A., Abbas Fakhari +5
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.1606.07322
openalex publication_date 2016/06/23 · openalex created_date 2016/07/22 · openalex updated_date 2026/07/28
In this paper we address the existence and ergodicity of non-hyperbolic attracting sets for a certain class of smooth endomorphisms on the solid torus. Such systems allow a formulation as a skew product system defined by planar diffeomorphisms have contraction on average which forced by any expanding circle map. These attractors are invariant graphs of upper semicontinuous maps which support exactly one SRB measure. In our approach, these skew product systems arising from iterated function systems generated by a finitely many weak contractive diffeomorphisms. Under some conditions including negative fiber Lyapunov exponents, we prove the existence of unique non-hyperbolic attracting invariant graphs for these systems which attract positive orbits of almost all initial points. Also, we prove that these systems are Bernoulli and therefore they are mixing. Moreover, these properties remain true under small perturbations in the space of endomorphisms on the solid torus.