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A criterion for mixed dynamics in two-dimensional reversible maps
1Imperial College, London SW7 2AZ, United Kingdom and Higher School of Economics-Nizhny Novgorod, B. Pecherskaya 25/12, 603155 Nizhny Novgorod, Russia.
Chaos (Woodbury, N.Y.)
|July 12, 2021
Summary
This study identifies conditions leading to non-conservative dynamics in reversible maps. It focuses on the presence of transverse and non-transverse homoclinic orbits, crucial for understanding complex system behavior.
Area of Science:
- Dynamical Systems and Chaos Theory
- Mathematical Physics
Background:
- Reversible maps are fundamental in classical mechanics and exhibit complex dynamics.
- Homoclinic orbits signify chaotic behavior and are key indicators of system instability.
Purpose of the Study:
- To establish the conditions under which reversible maps exhibit non-conservative dynamics.
- To analyze the role of transverse and non-transverse homoclinic orbits in inducing these dynamics.
Main Methods:
- Analysis of reversible dynamical systems.
- Investigation of homoclinic orbit structures (transverse and non-transverse).
- Derivation of mathematical conditions for non-conservative behavior.
Main Results:
- Provided specific criteria for non-conservative dynamics in reversible maps.
- Demonstrated the significance of both transverse and non-transverse homoclinic orbits.
- Established a link between geometric structures and dynamic properties.
Conclusions:
- The presence and type of homoclinic orbits are critical determinants of non-conservative dynamics in reversible maps.
- Understanding these conditions advances the study of chaotic and complex systems.
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