Control of escapes in two-degree-of-freedom open Hamiltonian systems

Area of Science:

• Nonlinear Dynamics
• Hamiltonian Systems
• Chaos Theory

Background:

• Chaotic scattering trajectories in Hamiltonian systems can lead to unpredictable system behavior.
• Controlling these trajectories is crucial for understanding and stabilizing complex dynamical systems.

Purpose of the Study:

• To investigate a novel continuous control technique for managing chaotic scattering trajectories.
• To demonstrate the avoidance of trajectory escape in two-degree-of-freedom Hamiltonian systems.

Main Methods:

• Development of a continuous control method using coupling forces.
• Introduction of forces between chaotic trajectories and periodic orbits.
• Numerical simulations to validate the control strategy.

Main Results:

• Successful control of all trajectories originating near the chaotic saddle's stable manifold.
• Demonstration of controlled jumps between unstable periodic orbits.
• Achievement of stable periodic orbits within Kolmogorov-Arnold-Moser islands.

Conclusions:

• The proposed continuous control technique effectively prevents the escape of chaotic trajectories.
• The method allows for guided transitions between different periodic orbits, enhancing system predictability.