``Stickiness'' in mappings and dynamical systems

Mathematics – Dynamical Systems

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

17

Scientific paper

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/2π . sin (2πxi) 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 very 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 behaviour 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.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

``Stickiness'' in mappings and dynamical systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with ``Stickiness'' in mappings and dynamical systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and ``Stickiness'' in mappings and dynamical systems will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-763830

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.