Instability of an area-preserving polynomial mapping
Copyright policy )Instability of an area-preserving polynomial mapping
Fixed points and eigencurves have been studied for the Henon-Heiles mapping:x′=x+a (y−y3),y′=y(x′−x′3). Eigencurves of order 21 proceed rapidly to infinity fora=1.78, but as ‘a’ decreases, they spiral around the origin repeatedly before escaping to infinity. Fixed pointsxfon thex-axis have been located for the range 1≤a≤2.4, for ordersn up to 100. Their locations vary continuously witha, as do the eigencurves, and hyperbolic points remain hyperbolic.
- Azusa Pacific University United States
- University of Alabama - USA United States
- Alabama Agricultural and Mechanical University United States
Henon-Heiles mapping, eigencurves, fixed points, homoclinic point, Software, source code, etc. for problems pertaining to global analysis, Strange attractors, chaotic dynamics of systems with hyperbolic behavior
Henon-Heiles mapping, eigencurves, fixed points, homoclinic point, Software, source code, etc. for problems pertaining to global analysis, Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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