Distribution of Periodic Orbits and the Homoclinic Tangle

Details Distribution of Periodic Orbits and the Homoclinic Tangle Distribution of Periodic Orbits and the Homoclinic Tangle

Dec 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996cemda..64..363c&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 64, Issue 4, pp.363-381

Astronomy and Astrophysics

Astronomy

6

Periodic Orbits, Stability And Instability, Homoclinic Tangle

Scientific paper

We study the distribution of regular and irregular periodic orbits on a Poincaré surface of section of a simple Hamiltonian system of 2 degrees of freedom. We explain the appearance of many lines of periodic orbits that form Farey trees. There are also lines that are very close to the asymptotic curves of the unstable periodic orbits. Some regular orbits, sometimes stable, are found inside the homoclinic tangle. We explain this phenomenon, which shows that the homoclinic tangle does not cover the whole area around an unstable orbit, but has gaps. Inside the lobes only irregular orbits appear, and some of them are stable. We conjecture that the opposite is also true, i.e. all irregular orbits are inside lobes.

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