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Shrimp-shape domains in a dissipative kicked rotator
Diego F M Oliveira1, Marko Robnik, Edson D Leonel
1CAMTP--Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia. diegofregolente@gmail.com
Chaos (Woodbury, N.Y.)
|January 10, 2012
Summary
Dissipation drastically alters the phase space of a kicked rotator, introducing stable fixed points and chaotic attractors. This study reveals self-similar structures within the chaotic regime, offering new insights into dissipative systems.
Area of Science:
- Nonlinear dynamics
- Chaos theory
- Statistical mechanics
Background:
- The kicked rotator is a paradigmatic model for studying chaotic dynamics.
- Understanding the influence of dissipation is crucial for real-world physical systems.
Purpose of the Study:
- To investigate the dynamical properties of a dissipative kicked rotator.
- To analyze the impact of dissipation on phase space structure and attractor behavior.
Main Methods:
- Numerical investigation of a two-dimensional parameter space.
- Analysis of Lyapunov exponents to identify chaotic and periodic regions.
- Characterization of phase space structures.
Main Results:
- Dissipation significantly modifies the phase space, replacing mixed structures with attracting fixed points and chaotic attractors.
- Infinite, self-similar, shrimp-shaped structures corresponding to periodic attractors were identified.
- These periodic structures are embedded within a large chaotic regime.
Conclusions:
- The dissipative kicked rotator exhibits complex dynamics with a rich interplay between periodic and chaotic behavior.
- The observed self-similar structures highlight the intricate organization within chaotic systems.
- Dissipation plays a critical role in shaping the long-term dynamics of the kicked rotator.
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