Finite-time rotation number: A fast indicator for chaotic dynamical structures |
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| Authors: | JD Szezech Jr AB Schelin IL Caldas SR Lopes PJ Morrison RL Viana |
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| Institution: | 1. Instituto de Física, Universidade de São Paulo, 5315-970, São Paulo, São Paulo, Brazil;2. Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, 84033-240, Ponta Grossa, Paraná, Brazil;3. Departamento de Física, Universidade Tecnológica Federal do Paraná, 80230-901, Curitiba, Paraná, Brazil;4. Departamento de Física, Universidade Federal do Paraná, 81531-990, Curitiba, Paraná, Brazil;5. Department of Physics, The University of Texas at Austin, Austin, TX 78712, United States |
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| Abstract: | Lagrangian coherent structures are effective barriers, sticky regions, that separate chaotic phase space regions of different dynamical behavior. The usual way to detect such structures is by calculating finite-time Lyapunov exponents. We show that similar results can be obtained for time-periodic systems by calculating finite-time rotation numbers, which are faster to compute. We illustrate our claim by considering examples of continuous- and discrete-time dynamical systems of physical interest. |
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