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Separatrix reconnection and periodic orbit annihilation in the Harper map
Satoshi Saito1, Yasuyuki Nomura, Kei-Ichi Hirose
1School of Engineering, Nagoya University, Nagoya 464-01, Japan.
Chaos (Woodbury, N.Y.)
|June 1, 1997
Summary
This study investigates chaotic accelerator orbits in the Harper map, revealing novel phenomena beyond standard theories. The research offers a rigorous analysis of area-preserving nontwist maps.
Area of Science:
- Nonlinear dynamics
- Chaos theory
- Mathematical physics
Background:
- Area-preserving nontwist maps exhibit complex dynamics.
- The Harper map is a model system for studying such dynamics.
- Standard theories like Kolmogorov-Arnol'd-Moser (KAM) have limitations.
Purpose of the Study:
- To investigate the structure of periodic accelerator orbits in the Harper map.
- To understand the underlying scenario of chaos in this specific map.
- To explore phenomena beyond the applicability of existing theories.
Main Methods:
- Rigorous mathematical analysis of the Harper map.
- Detailed investigation of its twist function, avoiding polynomial approximations.
- Examination of phase space dynamics over the entire variable range.
Main Results:
- Identified the structure of periodic accelerator orbits.
- Revealed novel dynamical phenomena.
- Demonstrated that these phenomena are outside the scope of KAM theory.
Conclusions:
- The Harper map provides a platform for studying novel chaotic behaviors.
- Rigorous analysis allows for a deeper understanding of nontwist map dynamics.
- This work extends the understanding of chaos in Hamiltonian systems.