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Diffusion and Lyapunov timescales in the Arnold model
Pablo M Cincotta1, Claudia M Giordano1, Ivan I Shevchenko2
1Grupo de Caos en Sistemas Hamiltonianos, Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata and Instituto de Astrofísica de La Plata (CONICET), B1900FWA La Plata, Argentina.
Physical Review. E
|November 18, 2022
Summary
This study investigates Lyapunov time and diffusion time in the Arnold Hamiltonian model
Area of Science:
- Dynamical systems
- Statistical mechanics
- Nonlinear dynamics
Background:
- The Arnold Hamiltonian model describes chaotic dynamics in conservative systems.
- Understanding dynamical timescales is crucial for predicting system behavior.
- The stochastic layer of resonant systems exhibits complex dynamics.
Purpose of the Study:
- To analyze and compare Lyapunov time and diffusion time within the Arnold Hamiltonian model's stochastic layer.
- To revisit Chirikov's formulation and analytical estimates for diffusion and Lyapunov times.
- To establish relationships between these two key dynamical timescales.
Main Methods:
- Revisiting Chirikov's formulation for analytical estimates.
- Deriving theoretical estimations for Lyapunov time.
- Conducting numerical experiments to compute both timescales for various parameter sets.
- Comparing analytical estimates with numerical results.
Main Results:
- Analytical estimates for diffusion and Lyapunov times show agreement with numerical computations for smaller parameter values.
- The case with equal parameters was numerically investigated.
- Relationships, including exponential and power laws, were established between diffusion time and Lyapunov time for large parameters.
Conclusions:
- The study validates analytical estimates for dynamical timescales in the Arnold Hamiltonian model.
- Established relationships provide insights into chaotic transport within the stochastic layer.
- Findings contribute to a deeper understanding of chaotic dynamics in Hamiltonian systems.
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