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Basin Entropy and Shearless Barrier Breakup in Open Non-Twist Hamiltonian Systems.
Leonardo C Souza1, Amanda C Mathias1, Pedro Haerter1
1Departamento de Física, Universidade Federal do Paraná, Curitiba 81531-990, PR, Brazil.
Entropy (Basel, Switzerland)
|August 26, 2023
Summary
We introduce basin entropy to quantify uncertainty in open Hamiltonian systems. This method reveals how a tunable parameter breaks the shearless barrier, preventing chaotic transport in non-twist maps.
Area of Science:
- Dynamical Systems
- Statistical Mechanics
- Fluid Dynamics
Background:
- Open Hamiltonian systems with area-preserving maps model incompressible planar flows.
- Escape basins in these systems exhibit fractal properties, indicating complex dynamics.
- A shearless barrier can prevent global chaotic transport, even with local violations of the twist condition.
Purpose of the Study:
- To introduce and utilize basin entropy as a novel concept for quantifying final-state uncertainty in dynamical systems.
- To demonstrate the breakup of the shearless barrier in open non-twist Hamiltonian systems.
- To establish a method for determining shearless barrier breakup by analyzing escape basin entropy variations.
Main Methods:
- Utilizing an area-preserving two-dimensional map to represent incompressible planar flows.
- Applying the concept of basin entropy to quantify the fractal nature of escape basins.
- Investigating the effect of a tunable parameter on escape basin entropy to identify barrier breakup.
Main Results:
- The fractal nature of escape basins is effectively revealed by basin entropy.
- Variations in basin entropy with a tunable parameter indicate the breakup of the shearless barrier.
- This provides a quantitative method to study the transition from regular to chaotic transport.
Conclusions:
- Basin entropy is a powerful tool for characterizing uncertainty and fractal structures in dynamical systems.
- The shearless barrier in open non-twist Hamiltonian systems can be dynamically broken.
- Understanding barrier breakup is crucial for predicting transport phenomena in such systems.
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