Unstable periodic orbits and the natural measure of nonhyperbolic chaotic saddles

Mukeshwar Dhamala, Ying-Cheng Lai

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26 Citations (Scopus)


Chaotic saddles are nonattracting dynamical invariant sets that physically lead to transient chaos. We examine the characterization of the natural measure by unstable periodic orbits for nonhyperbolic chaotic saddles in dissipative dynamical systems. In particular, we compare the natural measure obtained from a long: trajectory on the chaotic saddle to that evaluated from unstable periodic orbits embedded in it. Our systematic computations indicate that the periodic-orbit theory of the natural measure, previously shown to be valid only for hyperbolic chaotic sets, is applicable to nonhyperbolic chaotic saddles as well. [S1063-651X(99)08311-7].

Original languageEnglish
Pages (from-to)6176-6179
Number of pages4
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number5
Publication statusPublished - Nov 1999


  • open hydrodynamical flows
  • strange attractor
  • repellers
  • dimensions
  • boundaries
  • advection
  • sets


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