Geodesic
Conservation of Hyperbolic Tori in Hamiltonian Systems
Matematičeskie zametki, Tome 95 (2014) no. 2, pp. 227-233

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In 2000, Bolotin and Treshchev proposed an invariant definition of the hyperbolic torus, generalizing the traditional coordinate definition. Simultaneously, they conjectured that, under standard assumptions on its Diophantine properties, nondegeneracy, and analyticity, the hyperbolic torus is conserved in the case of small perturbations. This conjecture generalizes Graff's theorem. In the present paper, this conjecture is shown to be valid.
Keywords: hyperbolic torus, Hamiltonian system, Graff's theorem, frequency vector, KAM theory.
Mots-clés : Diophantine torus 
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     author = {A. G. Medvedev},
     title = {Conservation of {Hyperbolic} {Tori} in {Hamiltonian} {Systems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {227--233},
     publisher = {mathdoc},
     volume = {95},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_2_a5/}
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A. G. Medvedev. Conservation of Hyperbolic Tori in Hamiltonian Systems. Matematičeskie zametki, Tome 95 (2014) no. 2, pp. 227-233. http://geodesic.mathdoc.fr/item/MZM_2014_95_2_a5/