2023/05/06 by Sylvain Crovisier, Crovisier, Sylvain, Xiaodong Wang +5
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Advanced Differential Equations and Dynamical Systems
paper · pdf · doi:10.48550/arxiv.2305.03910
Bonatti and da Luz have introduced the class of multi-singular hyperbolic vector fields to characterize systems whose periodic orbits and singularities do not bifurcate under perturbation (called star vector fields). In this paper, we study the Sina"ı-Ruelle-Bowen measures for multi-singular hyperbolic vector fields: in a C1 open and C1 dense subset of multi-singular hyperbolic vector fields, each C^∞ one admits finitely many physical measures whose basins cover a full Lebesgue measure subset of the manifold. Similar results are also obtained for C1 generic multi-singular hyperbolic vector fields.