2026-04-13T03:46:39Zhttps://recercat.cat/oai/requestoai:recercat.cat:2117/11912025-07-16T23:54:18Zcom_2072_1033col_2072_452950
RECERCAT
author
Delshams Valdés, Amadeu
author
Llave Canosa, Rafael de la
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
http://creativecommons.org/licenses/by-nc-nd/2.5/es/ Open Access Attribution-NonCommercial-NoDerivs 2.5 Spain
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
Article