"Stickiness" in mappings and dynamical systems
- Autor(en)
- Rudolf Dvorak, G. Contopoulos, Ch Efthymiopoulos, N Voglis
- Abstrakt
We present results of a study of the so-called "stickiness" regions where orbits in mappings and dynamical systems stay for very long times near an island and then escape to the surrounding chaotic region. First we investigated the standard map in the form xi+1 = Xi+yi+1 and yi+1 = yi + K/2p ž sin (2pxi) with a stochasticity parameter K = 5, where only two islands of regular motion survive. We checked now many consecutive points - for special initial conditions of the mapping - stay within a certain region around the island. For an orbit on an invariant curve all the points remain forever inside this region, but outside the "last invariant curve" this number changes significantly even for every small changes in the initial conditions. In our study we found out that there exist two regions of "sticky" orbits around the invariant curves. A small region I confined by Cantori with small holes and an extended region II is outside these cantori which has an interesting fractal character. Investigating also the Sitnikov-Problem where two equally massive primary bodies move on elliptical Keplerian orbits, and a third massless body oscillates through the barycentre of the two primaries perpendicularly to the plane of the primaries - a similar behavior of the stickiness region was found. Although no clearly defined border between the two stickiness regions was found in the latter problem the fractal character of the outer region was confirmed. Œ 1998 Elsevier Science Ltd. All rights reserved.
- Organisation(en)
- Institut für Astrophysik
- Externe Organisation(en)
- National & Kapodistrian University of Athens, Academy of Athens
- Journal
- Planetary and Space Science
- Band
- 46
- Seiten
- 1567-1578
- Anzahl der Seiten
- 12
- ISSN
- 0032-0633
- Publikationsdatum
- 1998
- Peer-reviewed
- Ja
- ÖFOS 2012
- 103003 Astronomie
- Link zum Portal
- https://ucrisportal.univie.ac.at/de/publications/c50d706e-0ace-4591-b509-34be4b5fe8dd