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Fractal dimension in dissipative chaotic scattering.
Jesús M Seoane1, Miguel A F Sanjuán, Ying-Cheng Lai
1Nonlinear Dynamics and Chaos Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain. jesus.seoane@urjc.es
Summary
Weak dissipation
Area of Science:
- Complex systems
- Nonlinear dynamics
- Chaos theory
Background:
- Chaotic scattering systems are prevalent in physics.
- Understanding the impact of dissipation is crucial for real-world applications.
- Fractal dimensions characterize complex sets in chaotic systems.
Purpose of the Study:
- To investigate the influence of weak dissipation on chaotic scattering.
- To analyze the variation of fractal dimension with increasing dissipation.
- To uncover and explain a crossover phenomenon in this variation.
Main Methods:
- Developing a heuristic theory for the observed phenomenon.
- Conducting numerical simulations for both discrete-time and continuous-time systems.
- Analyzing the fractal dimension of singularities in scattering functions.
Main Results:
- A crossover phenomenon in fractal dimension was observed.
- The dimension decreases rapidly initially with dissipation, then slows down.
- The phenomenon is general across different scattering system types.
Conclusions:
- Dissipation significantly alters the fractal properties of chaotic scattering.
- The identified crossover phenomenon provides a new insight into dissipative chaos.
- Results are relevant for phenomena like particle advection in chaotic flows.
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