2026-04-13T14:23:30Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/11912025-07-16T23:54:18Zcom_2072_1033col_2072_452950

00925njm 22002777a 4500 dc Delshams Valdés, Amadeu author Llave Canosa, Rafael de la author 1999 We consider perturbations of integrable area preserving non twist maps of the annulus those are maps in which the twist condition changes sign These maps appear in a variety of applications notably transport in atmospheric Rossby waves We show in suitable parameter families the persistence of critical circles invariant circles whose rotation number is the maximum of all the rotation numbers of points in the map with Diophantine rotation number The parameter values with critical circles of frequency lie on a one dimensional analytic curve Furthermore we show a partial justication of Greenes criterion If analytic critical curves with Dio phantine rotation number exist the residue of periodic orbits that is one fourth of the trace of the derivative of the return map minus with rotation number converging to converges to zero exponen tially fast We also show that if analytic curves exist there should be periodic orbits approximating them and indicate how to compute them These results justify in particular conjectures put forward on the basis of numerical evidence in D del Castillo et al Phys D The proof of both results relies on the successive application of an iterative lemma which is valid also for d dimensional exact symplectic di eomorphisms The proof of this iterative lemma is based on the deformation method of singularity theory Hamiltonian dynamical systems Lagrangian functions Differentiable dynamical systems Hamiltonian systems Greene's criterion KAM theory Hamilton, Sistemes de Lagrange, Funcions de Sistemes dinàmics diferenciables Classificació AMS::37 Dynamical systems and ergodic theory::37E Low-dimensional dynamical systems Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics KAM theory and a partial justification of Greene's criterion for non-twist maps