Resonances in area-preserving maps
A resonance for an area-preserving map is a region of the phase space delineated by ''partial separatrices'', which are curves formed from pieces of stable and unstable manifold of hyperbolic periodic points. Each resonance has a central periodic orbit, which may be elliptic or hyperbolic with reflection. The partial separatrices have turnstiles like the partial barriers formed from cantori. In this paper we show that the areas of the resonances, as well as the turnstile areas, can be obtained from the actions of homoclinic orbits. Numerical results on the scaling of areas of resonances with period and parameter are given. If there are no invariant circles, the resonances appear to fill the phase space completely. Indeed, we prove that the collection of all hyperbolic cantori together with their partial barriers occupies zero area.
- Research Organization:
- Texas Univ., Austin (USA). Inst. for Fusion Studies
- DOE Contract Number:
- FG05-80ET53088
- OSTI ID:
- 5489294
- Report Number(s):
- DOE/ET/53088-237; IFSR-237; ON: DE86014390
- Country of Publication:
- United States
- Language:
- English
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