The squeeze effect in nonintegrable Hamiltonian systems
Weele, J.P. van der and Capel, H.W. and Valkering, T.P. and Post, T. (1988) The squeeze effect in nonintegrable Hamiltonian systems. Physica A: Theoretical and statistical physics, 147 (3). pp. 499532. ISSN 03784371

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Abstract:  In nonintegrable 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 twodimensional areapreserving 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 nonlinear 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/10.1016/03784371(88)901677 
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