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Characterization of transition to chaos with multiple positive Lyapunov exponents by unstable periodic orbits |
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| Authors: | Ruslan Davidchack Ying-Cheng Lai |
| Institution: | a Department of Physics and Astronomy, University of Kansas, Lawrence, KS 66045, USA b Departments of Mathematics and Electrical Engineering, Center for Systems Science and Engineering Research, Arizona State University, Tempe, AZ 85287, USA |
| Abstract: | We investigate how the transition to chaos with multiple positive Lyapunov exponents can be characterized by the set of infinite number of unstable periodic orbits embedded in the chaotic invariant set. We argue and provide numerical confirmation that the transition is generally accompanied by a nonhyperbolic behavior: unstable dimension variability. As a consequence, the Lyapunov exponents, except for the largest one, pass through zero continuously. |
| Keywords: | PACS classification codes: 05 45 Jn 05 45 Ac |
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