Renormalization of multidimensional Hamiltonian flows

被引：14

作者：

Khanin, Kostya

Dias, Joao Lopes

Marklof, Jens

机构：

[1] Univ Toronto, Dept Math, Toronto, ON M5S 3G3, Canada

[2] Univ Tecn Lisboa, ISEG, Dept Matemat, P-1200781 Lisbon, Portugal

[3] Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, England

来源：

NONLINEARITY | 2006年 / 19卷 / 12期

关键词：

D O I：

10.1088/0951-7715/19/12/001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：2727 / 2753

页数：27

共 50 条

[41] Scalar field theory renormalization in the Hamiltonian formulation
Contreras, C
Vergara, L
REVISTA MEXICANA DE FISICA, 2002, 48 : 77 - 79
[42] Basis optimization renormalization group for the quantum Hamiltonian
Sugihara, T
NUCLEAR PHYSICS B-PROCEEDINGS SUPPLEMENTS, 2002, 108 : 267 - 269
[43] UNIVERSALITY FROM RESONANCE RENORMALIZATION OF HAMILTONIAN MAPS
LICHTENBERG, AJ
PHYSICA D-NONLINEAR PHENOMENA, 1985, 14 (03) : 387 - 394
[44] THE ADIABATIC LIMIT FOR MULTIDIMENSIONAL HAMILTONIAN SYSTEMS
de Gosson, Maurice A.
JOURNAL OF GEOMETRY AND SYMMETRY IN PHYSICS, 2005, 4 : 19 - 43
[45] THE STABILITY OF MULTIDIMENSIONAL HAMILTONIAN-SYSTEMS
TKHAI, VN
PMM JOURNAL OF APPLIED MATHEMATICS AND MECHANICS, 1985, 49 (03): : 273 - 281
[46] On the chaotic diffusion in multidimensional Hamiltonian systems
P. M. Cincotta
C. M. Giordano
J. G. Martí
C. Beaugé
Celestial Mechanics and Dynamical Astronomy, 2018, 130
[47] STABILITY OF MULTIDIMENSIONAL HAMILTONIAN SYSTEMS.
Tkhai, V.N.
1600, (49):
[48] On the chaotic diffusion in multidimensional Hamiltonian systems
Cincotta, P. M.
Giordano, C. M.
Marti, J. G.
Beauge, C.
CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2018, 130 (01):
[49] Control of multidimensional integrable Hamiltonian systems
Kulp, CW
Tracy, ER
PHYSICAL REVIEW E, 2005, 72 (03)
[50] Hamiltonian flows on null curves
Musso, Emilio
Nicolodi, Lorenzo
NONLINEARITY, 2010, 23 (09) : 2117 - 2129

← 1 2 3 4 5 →