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2014 | OriginalPaper | Chapter

6. On Sensitive Dependence on Initial Conditions and Existence of Physical Measure for 3-Flows

Author : Vítor Araújo

Published in: Modeling, Dynamics, Optimization and Bioeconomics I

Publisher: Springer International Publishing

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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.

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Metadata
Title
On Sensitive Dependence on Initial Conditions and Existence of Physical Measure for 3-Flows
Author
Vítor Araújo
Copyright Year
2014
Book
Modeling, Dynamics, Optimization and Bioeconomics I

Print ISBN: 978-3-319-04848-2

Electronic ISBN: 978-3-319-04849-9

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-04849-9_6