For C^0 generic continuous maps or homeomorphisms on compact Riemannian manifolds, physical-like measures coincide with invariant measures supported on chain recurrent classes.
Bowen, Periodic orbits for hyperbolic flows, Amer
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Lyapunov irregular sets exhibit distributional chaos of type 1 under exponential specification and distinct ergodic Lyapunov spectra for Holder matrix cocycles.
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Physical-like Measures Coincide with Invariant Measures Supported on Chain Recurrent Classes
For C^0 generic continuous maps or homeomorphisms on compact Riemannian manifolds, physical-like measures coincide with invariant measures supported on chain recurrent classes.
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Laypunov Irregular Points With Distributional Chaos
Lyapunov irregular sets exhibit distributional chaos of type 1 under exponential specification and distinct ergodic Lyapunov spectra for Holder matrix cocycles.