Hierarchy of islands in conservative systems yields multimodal distributions of FTLEs |
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| Affiliation: | 1. Department of Zoology and Entomology, Rhodes University, Grahamstown 6140, South Africa;2. South African Institute for Aquatic Biodiversity, Somerset Street, Grahamstown 6139, South Africa;3. South African Environmental Observation Network, Egagasini Node, Martin Hammerschlag Way, Roggebaai 8012, South Africa;4. ASL Environmental Sciences Inc., Rajpur Place, Victoria V8M 1Z5, British Columbia, Canada;1. CIIMAR—Centro Interdisciplinar de Investigação Marinha e Ambiental, Universidade do Porto, 4050-123 Porto, Portugal;2. UCA—Universidad de Cádiz, 11510 Puerto Real, Spain;3. NCAR—National Center for Atmospheric Research, Boulder, CO 80305, USA;4. ICBAS—Instituto de Ciências Biomédicas Abel Salazar, Universidade do Porto, 4050-313 Porto, Portugal |
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| 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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