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Average exit time for volume-preserving maps.

J. D. Meiss1

  • 1Program in Applied Mathematics, University of Colorado, Boulder, Colorado 80304.

Chaos (Woodbury, N.Y.)
|March 1, 1997
PubMed
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We derived a formula for the average exit time of volume-preserving maps, relating it to the accessible region

Area of Science:

  • Dynamical systems and chaos theory.
  • Mathematical physics.

Background:

  • Understanding the long-term behavior of dynamical systems is crucial.
  • Survival probability analysis is key in characterizing system dynamics.

Purpose of the Study:

  • To establish a relationship between average exit time and accessible set measure for volume-preserving maps.
  • To provide a method for calculating the measure of accessible sets.
  • To analyze bounded orbits in specific dynamical systems.

Main Methods:

  • Derivation of a formula for average exit time based on set measures.
  • Application of the derived formula to the Henon quadratic map.

Main Results:

  • The average exit time over the entry set equals the ratio of accessible subset measure to entry set measure.

Related Experiment Videos

  • A simple bound for the algebraic decay exponent of survival probability was established.
  • The measure of bounded orbits for the Henon quadratic map was computed.

    • Conclusions:

    • The derived formula offers a novel tool for analyzing dynamical systems.
    • This work provides insights into the structure of accessible regions and bounded orbits.
    • The findings are applicable to understanding the decay of survival probability in chaotic systems.