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Hidden High Period Accelerator Modes in a Bouncer Model

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Nonlinear Dynamics: Materials, Theory and Experiments

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 173))

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Abstract

We characterized the influence of high period accelerator modes in the global dynamics of a non-dissipative Bouncer model . The dynamics of the system was investigated considering both complete and simplified approaches. Evaluating the average of the velocity over large ensembles of initial conditions for the complete mapping, we obtained particular ranges of the control parameter where high period accelerating structures are located. The position, influence and shape of the accelerator modes were obtained considering the symplectic mapping. Our results, lead us to infer that even for high period and less influent accelerator modes , the dynamics is globally affected for long time series, causing an anomalous diffusion , in compare with the regular Fermi acceleration .

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Acknowledgments

ALPL acknowledges FAPESP and CNPq for financial support. ILC thanks FAPESP (2011/19296-1) and EDL thanks FAPESP (2012/23688-5), CNPq and CAPES, Brazilian agencies.

Author information

Authors and Affiliations

  1. Universidade Tecnológica Federal do Paraná, Pato Branco, Paraná, Brazil

    Tiago Kroetz

  2. Departamento de Física, Universidade Estadual Paulista, Rio Claro, São Paulo, Brazil

    André L. P. Livorati & Edson D. Leonel

  3. Instituto de Física, Universidade de São Paulo, São Paulo, Brazil

    Iberê L. Caldas

Authors
  1. Tiago Kroetz
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  2. André L. P. Livorati
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  3. Edson D. Leonel
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  4. Iberê L. Caldas
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Corresponding author

Correspondence to Tiago Kroetz .

Editor information

Editors and Affiliations

  1. Physique des systèmes dynamiques, Université Libre de Bruxelles, Brussels, Belgium

    Mustapha Tlidi

  2. Universidad de Chile, Santiago, Chile

    Marcel. G. Clerc

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Kroetz, T., Livorati, A.L.P., Leonel, E.D., Caldas, I.L. (2016). Hidden High Period Accelerator Modes in a Bouncer Model. In: Tlidi, M., Clerc, M. (eds) Nonlinear Dynamics: Materials, Theory and Experiments. Springer Proceedings in Physics, vol 173. Springer, Cham. https://doi.org/10.1007/978-3-319-24871-4_13

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