Invariant spectra in Hamiltonian systems.

Details Invariant spectra in Hamiltonian systems. Invariant spectra in Hamiltonian systems.

Dec 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995a%26a...304..374c&link_type=abstract

Astronomy and Astrophysics, v.304, p.374

Astronomy and Astrophysics

Astrophysics

13

Galaxy: Kinematics And Dynamics, Chaos, Stellar Dynamics

Scientific paper

We define a "stretching number" on a Poincare surface of section for Hamiltonian systems of two degrees of freedom. This is similar to what others call a "local" or "effective" Lyapunov exponent, but it is defined for one iteration only. The distribution of the successive stretching numbers forms a spectrum, which is invariant with respect to (a) the initial conditions along an orbit and the direction of the deviation from this orbit and (b) the initial conditions of orbits in the same chaotic region, or the initial conditions along a given invariant curve. The density of the consequents in the chaotic region is uniform. But if we divide the range of stretching numbers in intervals, according to their size, the corresponding consequents fill separate parts of the Poincare surface of section, which are invariant and define lines of constant a, which are probably fractals. These invariant parts are in general asymmetric, but in exceptional cases they are symmetric.

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