Area-Preserving Maps

  • Linda E. Reichl
Part of the Institute for Nonlinear Science book series (INLS)


Area-preserving maps provide the simplest and most accurate means to visualize and quantify the behavior of conservative systems with two degrees of freedom. Such maps can be iterated on even the smallest computers with great accuracy, and provide beautiful pictures of the mechanisms at play during the transition to chaos. The class of area-preserving maps we will study in this chapter are the so-called twist maps. When an integrable twist map is rendered nonintegrable by a small perturbation, resonance can occur and degenerate lines of fixed points in the integrable map are changed to finite chains of alternating hyperbolic and elliptic fixed points surrounded by nonlinear resonance zones. As the strength of the perturbation is increased, the resonance zones grow, and can overlap and form a chaotic sea.


Periodic Orbit Periodic Point Unstable Manifold Symmetry Line Chaotic Region 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Linda E. Reichl
    • 1
  1. 1.Department of Physics and Center for Statistical Mechanics and Complex SystemsUniversity of Texas at AustinAustinUSA

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