The squeeze effect in non-integrable Hamiltonian systems

Share/Save/Bookmark

Weele van der, J.P. and Capel, H.W. and Valkering, T.P. and Post, T. (1988) The squeeze effect in non-integrable Hamiltonian systems. Physica A: Theoretical and statistical physics, 147 (3). pp. 499-532. ISSN 0378-4371

[img]
Preview
PDF
1418Kb
Abstract:In non-integrable Hamiltonian systems (represented by mappings of the plane) the stable island around an elliptic fixed point is generally squeezed into the fixed point by three saddle points, when the rotation number ρ of the motion at the fixed point approaches 1/3. At ρ=1/3 the island is reduced to one single point.
A detailed investigation of this squeeze effect, and some of its global implications, is presented by means of a typical two-dimensional area-preserving map. In particular, it turns out that the squeeze effect occurs in any mapping for which the Taylor expansion around the fixed point contains a quadratic term, whereas it does not occur if the first non-linear term is cubic. We illustrate this with two physical examples: a compass needle in an oscillating field, showing the squeeze effect, and a ball which bounces on a vibrating plane, for which the squeeze effect does not occur.
Item Type:Article
Copyright:© 1988 Elsevier
Link to this item:http://purl.utwente.nl/publications/70317
Official URL:http://dx.doi.org/10.1016/0378-4371(88)90167-7
Export this item as:BibTeX
EndNote
HTML Citation
Reference Manager

 

Repository Staff Only: item control page