Area Preserving Maps

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

Abstract

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 non-integrable 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, can overlap and form a chaotic sea.

Keywords

Periodic Orbit Period Doubling Bifurcation Chaotic Region Bernoulli Shift Boundary Circle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • L. E. Reichl
    • 1
  1. 1.Center for Statistical Mechanics and Complex Systems, Department of PhysicsUniversity of Texas at AustinAustinUSA

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