Renormalization of mulitdimensional Hamiltonian flows

K Khanin; JL Dias; J Marklof

doi:10.1088/0951-7715/19/12/001

Renormalization of mulitdimensional Hamiltonian flows

K Khanin, JL Dias, J Marklof

Research output: Contribution to journal › Article (Academic Journal) › peer-review

14 Citations (Scopus)

Abstract

We construct a renormalization operator acting on the space of analytic Hamiltonians defined on T*T-d, d >= 2, based on the multidimensional continued fractions algorithm developed by the authors. We show convergence of orbits of the operator around integrable Hamiltonians satisfying a non-degeneracy condition. This in turn yields a new proof of a KAM-type theorem on the stability of diophantine invariant tori.

Translated title of the contribution	Renormalization of mulitdimensional Hamiltonian flows
Original language	English
Pages (from-to)	2727 - 2753
Number of pages	27
Journal	Nonlinearity
Volume	19 (12)
DOIs	https://doi.org/10.1088/0951-7715/19/12/001
Publication status	Published - Dec 2006

Bibliographical note

Publisher: IOP Publishing Ltd
Other identifier: IDS number 112LX

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10.1088/0951-7715/19/12/001

http://ej.iop.org/links/ruZOnc3rw/BGLiwK7i2xG9qxHeav5vpA/non6_12_001.pdf

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title = "Renormalization of mulitdimensional Hamiltonian flows",

abstract = "We construct a renormalization operator acting on the space of analytic Hamiltonians defined on T*T-d, d >= 2, based on the multidimensional continued fractions algorithm developed by the authors. We show convergence of orbits of the operator around integrable Hamiltonians satisfying a non-degeneracy condition. This in turn yields a new proof of a KAM-type theorem on the stability of diophantine invariant tori.",

author = "K Khanin and JL Dias and J Marklof",

note = "Publisher: IOP Publishing Ltd Other identifier: IDS number 112LX",

year = "2006",

month = dec,

doi = "10.1088/0951-7715/19/12/001",

language = "English",

volume = "19 (12)",

pages = "2727 -- 2753",

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TY - JOUR

T1 - Renormalization of mulitdimensional Hamiltonian flows

AU - Khanin, K

AU - Dias, JL

AU - Marklof, J

N1 - Publisher: IOP Publishing Ltd Other identifier: IDS number 112LX

PY - 2006/12

Y1 - 2006/12

N2 - We construct a renormalization operator acting on the space of analytic Hamiltonians defined on T*T-d, d >= 2, based on the multidimensional continued fractions algorithm developed by the authors. We show convergence of orbits of the operator around integrable Hamiltonians satisfying a non-degeneracy condition. This in turn yields a new proof of a KAM-type theorem on the stability of diophantine invariant tori.

AB - We construct a renormalization operator acting on the space of analytic Hamiltonians defined on T*T-d, d >= 2, based on the multidimensional continued fractions algorithm developed by the authors. We show convergence of orbits of the operator around integrable Hamiltonians satisfying a non-degeneracy condition. This in turn yields a new proof of a KAM-type theorem on the stability of diophantine invariant tori.

U2 - 10.1088/0951-7715/19/12/001

DO - 10.1088/0951-7715/19/12/001

M3 - Article (Academic Journal)

SN - 1361-6544

VL - 19 (12)

SP - 2727

EP - 2753

JO - Nonlinearity

JF - Nonlinearity

ER -

Renormalization of mulitdimensional Hamiltonian flows

Abstract

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