English

Normal form \`a la Moser for diffeomorphisms and generalization of R\"ussmann's translated curve theorem to higher dimension

Dynamical Systems 2018-03-16 v1

Abstract

We prove a discrete time analogue of 1967 Moser's normal form of real analytic perturbations of vector fields possessing an invariant, reducible, Diophantine torus; in the case of diffeomorphisms too, the persistence of such an invariant torus is a phenomenon of finite co-dimension. Under convenient non-degeneracy assumptions on the diffeomorphisms under study (torsion property for example), this co-dimension can be reduced. As a by-product we obtain generalizations of R\"ussmann's translated curve theorem in any dimension, by a technique of elimination of parameters.

Keywords

Cite

@article{arxiv.1608.03500,
  title  = {Normal form \`a la Moser for diffeomorphisms and generalization of R\"ussmann's translated curve theorem to higher dimension},
  author = {Jessica Elisa Massetti},
  journal= {arXiv preprint arXiv:1608.03500},
  year   = {2018}
}

Comments

arXiv admin note: text overlap with arXiv:1512.01486, arXiv:1511.02733