Local Gram-Schmidt and covariant Lyapunov vectors and exponents for three harmonic oscillator problems
Abstract
We compare the Gram-Schmidt and covariant phase-space-basis-vector descriptions for three time-reversible harmonic oscillator problems, in two, three, and four phase-space dimensions respectively. The two-dimensional problem can be solved analytically. The three-dimensional and four-dimensional problems studied here are simultaneously chaotic, time-reversible, and dissipative. Our treatment is intended to be pedagogical, for use in an updated version of our book on Time Reversibility, Computer Simulation, and Chaos. Comments are very welcome.
- Publication:
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Communications in Nonlinear Science and Numerical Simulations
- Pub Date:
- February 2012
- DOI:
- arXiv:
- arXiv:1106.2367
- Bibcode:
- 2012CNSNS..17.1043H
- Keywords:
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- Nonlinear Sciences - Chaotic Dynamics
- E-Print:
- 25 pages with 12 figures