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Rapid geometrical chaotization in slow-fast Hamiltonian systems
A V Artemyev1, A I Neishtadt2, L M Zelenyi1
1Space Research Institute RAS, Moscow 117997, Russia.
Summary
A new mechanism rapidly destroys adiabaticity in Hamiltonian systems, causing fast chaotization across large phase volumes. This contrasts with typical slow, diffusive destruction, offering new insights into chaotic dynamics.
Area of Science:
- Physics
- Nonlinear Dynamics
- Chaos Theory
Background:
- Adiabaticity destruction in Hamiltonian systems is typically a slow, diffusive process.
- Understanding rapid chaotization mechanisms is crucial for analyzing complex dynamical systems.
Purpose of the Study:
- To demonstrate a novel mechanism for rapid adiabaticity destruction in Hamiltonian systems.
- To investigate the role of separatrix asymmetry in inducing fast chaotization.
Main Methods:
- Analysis of a two-degree-of-freedom Hamiltonian system with a separatrix.
- Examination of geometrical jumps in the adiabatic invariant.
Main Results:
- A new mechanism for rapid adiabaticity destruction was identified.
- Separatrix asymmetry leads to geometrical jumps of the adiabatic invariant.
- This mechanism causes very fast chaotization in a large phase volume.
Conclusions:
- The identified mechanism provides a new pathway for rapid chaotization in Hamiltonian systems.
- Geometrical jumps of the adiabatic invariant are key to this fast chaotic behavior.
- The findings have implications for understanding charged particle motion in specific electromagnetic fields.
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