2000 character limit reached
A characterization of physical measures for systems with mixed central behavior
Published 16 May 2024 in math.DS | (2405.10144v3)
Abstract: We show that the existence of physical measures for $C\infty$ smooth instances of certain partially hyperbolic dynamics, both continuous and discrete, exhibiting mixed behavior (positive and negative Lyapunov exponents) along the central non-uniformly hyperbolic multidimensional invariant direction, is equivalent to the existence of certain types of ``regular points'' on positive volume subsets, including Lyapunov regular points. This encompasses the $C3$ robust class of multidimensional non-hyperbolic attractors obtained by Viana, and the $C1$ robust classes of $3$-sectionally hyperbolic wild strange attractors presented by Shilnikov and Turaev, providing necessary and sufficient conditions for the existence of ergodic hyperbolic physical measures on these and other dynamical systems.
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