Almost stable regions for an area-preserving mapping

Details Almost stable regions for an area-preserving mapping Almost stable regions for an area-preserving mapping

Jun 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989cemda..46..129b&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 46, no. 2, 1989, p. 129-145.

Mathematics

Celestial Mechanics, Computer Aided Mapping, Mapping, Cyclic Accelerators, Fixed Points (Mathematics), Iterative Solution, Orbit Perturbation, Particle Beams

Scientific paper

The area preserving mapping x-prime = x + a(y - y-cubed), y-prime = y - a(x-prime - x-prime-cubed), for a between values of 0.3 and 2.0 has been studied to locate approximately the x-axis points bounding almost stable regions. For each value of a, these are fixed points with variational trace just greater than 2.0. Transition to chaos can occur rapidly as a increases (with n/k fixed).

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