Proof of Lyapunov exponent pairing for systems at constant kinetic energy.

@article{Dettmann1996ProofOL,
  title={Proof of Lyapunov exponent pairing for systems at constant kinetic energy.},
  author={Dettmann and Morriss},
  journal={Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics},
  year={1996},
  volume={53 6},
  pages={
          R5545-R5548
        }
}
  • Dettmann, Morriss
  • Published 1 June 1996
  • Mathematics, Computer Science
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
We present a proof that a system consisting of any finite number of particles that move under the action of a scalar potential at constant kinetic energy exhibits conjugate pairing of Lyapunov exponents; that is, the Lyapunov exponents come in pairs, which sum to the same constant. This result generalizes previous results, because it is independent of the size of the system. @S1063-651X~96!51206-7# 
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Introduction Foreward by Tudor Ratiu and Richard Cushman Preliminaries Differential Theory Calculus on Manifolds Analytical Dynamics Hamiltonian and Lagrangian Systems Hamiltonian Systems with…