Abstract
After reviewing known results on sensitiveness and also on robustness of attractors together with observations on their proofs, we show that for attractors of three-dimensional flows, robust chaotic behavior (meaning sensitiveness to initial conditions for the past as well for the future for all nearby flows) is equivalent to the existence of certain hyperbolic structures. These structures, in turn, are associated to the existence of physical measures. In short in low dimensions, robust chaotic behavior for smooth flows ensures the existence of a physical measure.KeywordsPeriodic OrbitRegular OrbitSensitive DependenceLorenz AttractorStable FoliationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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