Stable Ergodicity and Accessibility for certain Partially Hyperbolic\n Diffeomorphisms with Bidimensional Center Leaves

2016/02/29 by Vanderlei Horita, Horita, Vanderlei, Martı́n Sambarino +1 · 1 citation
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.1603.00053

openalex publication_date 2016/02/29 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28

Abstract

We consider classes of partially hyperbolic diffeomorphism f:M\→ M with\nsplitting TM=E^s\⊕ E^c\⊕ E^u and \dim E^c=2. These classes include\nfor instance (perturbations of) the product of Anosov and conservative surface\ndiffeomorphisms, skew products of surface diffeomorphisms over Anosov,\npartially hyperbolic symplectomorphisms on manifolds of dimension four with\nbidimensional center foliation whose center leaves are all compact. We prove\nthat accessibility holds in these classes for C¹ open and C^r dense\nsubsets and moreover they are stably ergodic.\n

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