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Universality of algebraic laws in hamiltonian systems
1Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, 09210-170, Santo André, SP, Brazil. roberto.venegeroles@ufabc.edu.br
Physical Review Letters
|March 5, 2009
Summary
We found universal exponents of 3/2 for trajectory trapping in Hamiltonian systems with unbounded phase space. This applies to recurrence time statistics and superdiffusion, supported by analytical and experimental data.
Area of Science:
- Complex systems
- Statistical mechanics
- Dynamical systems theory
Background:
- Hamiltonian mixed systems exhibit complex dynamics.
- Unbounded phase space systems show characteristic decay of recurrence time statistics (gamma) and superdiffusion (beta).
Purpose of the Study:
- To investigate and conjecture universal exponents for trajectory trapping in Hamiltonian mixed systems.
- To analyze systems with both unbounded and bounded phase spaces.
Main Methods:
- Analytical derivation of exponents for a wide class of area-preserving maps.
- Review and integration of existing simulation and experimental data.
Main Results:
- Conjectured universal exponents gamma = beta = 3/2 for trajectory trapping in systems with unbounded phase space.
- Established an interval 3/2 <= gamma_b <= 3 for trapping exponents in systems with bounded phase space.
Conclusions:
- The findings suggest a universal behavior in trajectory trapping for Hamiltonian mixed systems.
- The conjectured exponents are supported by analytical results and external experimental evidence.
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