Dynamical properties of a dissipative discontinuous map: A scaling investigation |
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Authors: | R Aguilar-Sánchez Edson D Leonel JA Méndez-Bermúdez |
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Institution: | 1. Facultad de Ciencias Químicas, Benemérita Universidad Autónoma de Puebla, Puebla 72570, Mexico;2. Departamento de Física, UNESP – Univ. Estadual Paulista, Av. 24A, 1515, Bela Vista, 13506-900 Rio Claro, SP, Brazil;3. Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico |
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Abstract: | The effects of dissipation on the scaling properties of nonlinear discontinuous maps are investigated by analyzing the behavior of the average squared action 〈I2〉 as a function of the n-th iteration of the map as well as the parameters K and γ , controlling nonlinearity and dissipation, respectively. We concentrate our efforts to study the case where the nonlinearity is large; i.e., K?1. In this regime and for large initial action I0?K, we prove that dissipation produces an exponential decay for the average action 〈I〉. Also, for I0≅0, we describe the behavior of 〈I2〉 using a scaling function and analytically obtain critical exponents which are used to overlap different curves of 〈I2〉 onto a universal plot. We complete our study with the analysis of the scaling properties of the deviation around the average action ω. |
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Keywords: | Scaling Discontinuous map Dissipation |
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