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Systems with escapes.

G Contopoulos¹, M Harsoula

¹Research Center of Astronomy, Academy of Athens, Athens, Greece. gcontop@cc.uoa.gr

Annals of the New York Academy of Sciences

|June 28, 2005

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This study investigates escape dynamics in conservative systems, revealing fractal basin structures for escapes to infinity and energy-dependent escape patterns into black holes. Understanding these complex dynamics is crucial for predicting system behavior.

Area of Science:

Physics
Dynamical Systems
Astrophysics

Background:

Conservative dynamical systems with two degrees of freedom exhibit complex escape behaviors.
Area-preserving properties are violated during escape events, leading to non-trivial basin structures.

Purpose of the Study:

To analyze the fractal nature of escape basins to infinity in simple Hamiltonian systems.
To investigate the influence of energy levels on escape trajectories into two fixed black holes.
To characterize unstable periodic orbits and their role in shaping escape sets.

Main Methods:

Utilizing surfaces of section to visualize and analyze orbital dynamics.
Simulating orbits to identify initial conditions leading to escape.
Examining the dependence of escape set morphology on system energy and unstable periodic orbits.

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Main Results:

Identified spiral fractal sets for initial conditions leading to escape to infinity after multiple surface of section intersections.
Demonstrated that the geometry of escape basins into black holes is contingent upon system energy.
Characterized simple periodic orbits and their transformations across different energy regimes.

Conclusions:

Escape dynamics in conservative systems are characterized by fractal structures and sensitive dependence on initial conditions.
The presence of black holes significantly alters escape basin topology, influenced by unstable periodic orbits.
Energy is a critical parameter governing the complex patterns of escape in these systems.