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Secondary nontwist phenomena in area-preserving maps
1Instituto de Física, Universidade de São Paulo, São Paulo, 05315-970 São Paulo, Brazil. cabud@if.usp.br
Chaos (Woodbury, N.Y.)
|October 2, 2012
Summary
This study numerically investigates secondary shearless tori in dynamical systems, revealing their emergence near tripling and quadrupling bifurcations. These findings enhance our understanding of complex behaviors in nontwist maps.
Area of Science:
- Dynamical Systems
- Nonlinear Dynamics
- Chaos Theory
Background:
- Nontwist maps exhibit phenomena like reconnection and periodic-orbit collisions.
- Secondary shearless tori were recently predicted near tripling bifurcations of elliptic fixed points.
Purpose of the Study:
- To numerically explore the creation of periodic orbits via saddle-center bifurcations.
- To investigate the occurrence of secondary shearless tori in dynamical systems.
Main Methods:
- Application of a numerical procedure to find internal rotation number profiles.
- Analysis of twist and nontwist standard maps.
Main Results:
- Numerical procedure highlights periodic orbit creation within stability islands.
- Atypical secondary shearless tori are found near both tripling and quadrupling bifurcations.
Conclusions:
- Confirms and extends analytical predictions for secondary shearless tori.
- Demonstrates the broader occurrence of secondary shearless tori beyond tripling bifurcations.
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