Deformations of Two-Dimensional Dissipative Maps

摘要

Necessary and sufficient conditions are obtained for persistency under analytic perturbations of orbits of the dissipative integrable map yn+1 = yn xn+1 = bxn + yn (mod. 1), b 1. An analytical numerical study of constant Jacobian maps of the 2-torus is performed to check the range of applicability of the deformation stability criteria, and to test the criteria and the deformation ideas in domains where it is not proven they can apply. Focusing evolution is treated, and it is suggested that large scale stochastic regimes can be interpreted as deformations of exactly solvable strongly dissipative systems.