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The brief time-reversibility of the local Lyapunov exponents for a small chaotic Hamiltonian system

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  • Waldner, Franz
  • Hoover, William G.
  • Hoover, Carol G.

Abstract

We consider the local (instantaneous) Lyapunov spectrum for a four-dimensional Hamiltonian system. Its stable periodic motion can be reversed for long times. Its unstable chaotic motion, with two symmetric pairs of exponents, cannot. In the latter case reversal occurs for more than a thousand fourth-order Runge–Kutta time steps, followed by a transition to a new set of paired Lyapunov exponents, unrelated to those seen in the forward time direction. The relation of the observed chaotic dynamics to the Second Law of Thermodynamics is discussed.

Suggested Citation

  • Waldner, Franz & Hoover, William G. & Hoover, Carol G., 2014. "The brief time-reversibility of the local Lyapunov exponents for a small chaotic Hamiltonian system," Chaos, Solitons & Fractals, Elsevier, vol. 60(C), pages 68-76.
    • Handle: RePEc:eee:chsofr:v:60:y:2014:i:c:p:68-76
    DOI: 10.1016/j.chaos.2014.01.006
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    References listed on IDEAS

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    1. Waldner, Franz & Klages, Rainer, 2012. "Symmetric Jacobian for local Lyapunov exponents and Lyapunov stability analysis revisited," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 325-340.
    2. Lebowitz, Joel L., 1999. "Microscopic origins of irreversible macroscopic behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 263(1), pages 516-527.
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