Frobenius-perron resonances for maps with a mixed phase space

Area of Science:

• * Physics
• * Dynamical Systems Theory
• * Quantum Mechanics

Background:

• * Resonances of the time evolution (Frobenius-Perron) operator are crucial for understanding classical, semiclassical, and quantum dynamics.
• * Efficient methods for determining these resonances are needed, especially for complex Hamiltonian systems with mixed chaotic and regular behaviors.

Purpose of the Study:

• * To present a powerful and efficient method for identifying resonances and associated phase space structures.
• * To address the demand for resonance detection in dynamical systems.

Main Methods:

• * Truncating the Frobenius-Perron operator (P) to a finite matrix.
• * Applying this matrix representation to identify resonances and their corresponding phase space structures.

Main Results:

• * The developed method successfully identifies resonances.
• * The method also reveals the associated phase space structures.
• * The approach is validated on a prototypical dynamical system, demonstrating its effectiveness.

Conclusions:

• * Finite matrix truncation of the Frobenius-Perron operator is an effective technique for resonance identification.
• * This method provides insights into the interplay between classical, semiclassical, and quantum dynamics.
• * The study offers a valuable tool for analyzing complex dynamical systems.