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Published on: February 22, 2018
Intrinsic stickiness and chaos in open integrable billiards: tiny border effects
1Departamento de Física, Universidade Federal do Paraná, 81531-990 Curitiba, PR, Brazil.
Summary
Rounding border effects in open integrable billiards create sticky motion and chaos. Even small rounded borders significantly influence escape times and emission angles, revealing complex dynamics.
Area of Science:
- Physics
- Dynamical Systems
- Statistical Mechanics
Background:
- Open integrable billiards exhibit complex dynamics influenced by boundary conditions.
- Escape-time statistics and emission angles are key to understanding particle trajectories.
Purpose of the Study:
- To analyze the impact of rounded border effects at the escape point of open integrable billiards.
- To investigate the generation of stickiness, chaos, and self-similar structures in escape dynamics.
Main Methods:
- Analysis of escape-time statistics and emission angles in a rectangular billiard model.
- Simulation of semicircular escape point shapes and varying border rounding.
Main Results:
- Rounded borders induce "backgammon"-like stripes of initial conditions, leading to stickiness and chaos.
- Tiny rounded borders (0.1%) generate sticky motion with a power-law decay (γ(esc)=1.27).
- Larger borders (>10%) result in escape times associated with chaotic motion.
Conclusions:
- Border rounding is crucial for generating rich dynamics in open billiards.
- Marginal unstable periodic orbits contribute to escape exponents between 1 and 2.
- The study highlights the sensitivity of dynamical systems to boundary conditions.
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