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Hierarchy of islands in conservative systems yields multimodal distributions of FTLEs

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  • Harle, M.
  • Feudel, U.

Abstract

We investigate the motion in a chaotic layer of conservative systems using finite time Lyapunov exponents (FTLEs). For long finite time spans we find the distributions of FTLEs to be multimodal. Due to stickiness near islands of regular motion, the trajectory can spend a long time in their vicinity. The higher the order of an island in the hierarchy of islands, the smaller is the value of the largest FTLE. Using this connection, we explain the occurrence of multimodal distributions of FTLEs as a result of an overlap of individual distributions of FTLEs, each corresponding to the motion near islands of different orders.

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  • Harle, M. & Feudel, U., 2007. "Hierarchy of islands in conservative systems yields multimodal distributions of FTLEs," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 130-137.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:1:p:130-137
    DOI: 10.1016/j.chaos.2005.09.031
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    1. Feudel, F. & Witt, A. & Gellert, M. & Kurths, J. & Grebogi, C. & Sanjuán, M.A.F., 2005. "Intersections of stable and unstable manifolds: the skeleton of Lagrangian chaos," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 947-956.
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    Cited by:

    1. Cetin, Kivanc & Tirnakli, Ugur & Oliveira, Diego F.M. & Leonel, Edson D., 2024. "Statistical mechanical characterization of billiard systems," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

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