Whiskered KAM tori of conformally symplectic systems
Mathematics Research Reports, Volume 1 (2020) , pp. 15-29.

We investigate the existence of whiskered tori in some dissipative systems, called conformally symplectic systems, having the property that they transform the symplectic form into a multiple of itself. We consider a family f μ of conformally symplectic maps which depends on a drift parameter μ.

We fix a Diophantine frequency of the torus and we assume to have a drift μ 0 and an embedding of the torus K 0 , which satisfy approximately the invariance equation f μ 0 K 0 =K 0 T ω (where T ω denotes the shift by ω). We also assume to have a splitting of the tangent space at the range of K 0 into three bundles. We assume that the bundles are approximately invariant under Df μ 0 and the derivative satisfies some rate conditions.

Under suitable nondegeneracy conditions, we prove that there exist μ , K invariant under f μ , close to the original ones, and a splitting which is invariant under Df μ . The proof provides an efficient algorithm to construct whiskered tori. Full details of the statements and proofs are given in [10].

Received: 2019-01-23
Accepted: 2019-05-21
Published online: 2020-06-30
DOI: https://doi.org/10.5802/mrr.4
Classification: 70K43,  70K20,  34D30
Keywords: Whiskered tori, Conformally symplectic systems, KAM theory.
@article{MRR_2020__1__15_0,
     author = {Renato C.  Calleja and Alessandra Celletti and Rafael de la Llave},
     title = {Whiskered KAM tori of conformally symplectic systems},
     journal = {Mathematics Research Reports},
     publisher = {MathOA foundation},
     volume = {1},
     year = {2020},
     pages = {15-29},
     doi = {10.5802/mrr.4},
     language = {en},
     url = {mrr.centre-mersenne.org/item/MRR_2020__1__15_0/}
}
Renato C.  Calleja; Alessandra Celletti; Rafael de la Llave. Whiskered KAM tori of conformally symplectic systems. Mathematics Research Reports, Volume 1 (2020) , pp. 15-29. doi : 10.5802/mrr.4. https://mrr.centre-mersenne.org/item/MRR_2020__1__15_0/

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