The KAM theorem and renormalization group

被引：5
|
作者：
De Simone, E. [1 ]
Kupiainen, A. [1 ]
机构：
[1] Dept Math & Stat, Helsinki 00014, Finland
来源：
ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2009年 / 29卷
关键词：
TORI;
D O I：
10.1017/S0143385708080450
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We give an elementary proof of the analytic KAM theorem by reducing it to a Picard iteration of a certain PDE with quadratic nonlinearity, the so-called Polchinski renormalization group equation studied in quantum field theory.
引用
收藏
页码：419 / 431
页数：13
相关论文
共 50 条
  • [1] A renormalization group for Hamiltonians, with applications to KAM tori
    Koch, H
    [J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1999, 19 : 475 - 521
  • [2] A Renormalization proof of the KAM theorem for non-analytic perturbations
    De Simone, Emiliano
    [J]. REVIEWS IN MATHEMATICAL PHYSICS, 2007, 19 (06) : 639 - 675
  • [3] An Approximate KAM-Renormalization-Group Scheme for Hamiltonian Systems
    C. Chandre
    H. R. Jauslin
    G. Benfatto
    [J]. Journal of Statistical Physics, 1999, 94 : 241 - 251
  • [4] An approximate KAM-renormalization-group scheme for Hamiltonian systems
    Chandre, C
    Jauslin, HR
    Benfatto, G
    [J]. JOURNAL OF STATISTICAL PHYSICS, 1999, 94 (1-2) : 241 - 251
  • [5] KAM Theory as a Limit of Renormalization
    Dias, Joao Lopes
    [J]. DYNAMICS, GAMES AND SCIENCE I, 2011, 1 : 253 - 270
  • [6] KAM THEOREM AND ISO-ENERGETIC KAM THEOREM ON POISSON MANIFOLD
    Qian, Weichao
    [J]. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2023, 13 (02): : 1088 - 1107
  • [7] Generalized Central Limit Theorem and Renormalization Group
    Calvo, Ivan
    Cuchi, Juan C.
    Esteve, Jose G.
    Falceto, Fernando
    [J]. JOURNAL OF STATISTICAL PHYSICS, 2010, 141 (03) : 409 - 421
  • [8] Generalized Central Limit Theorem and Renormalization Group
    Iván Calvo
    Juan C. Cuchí
    José G. Esteve
    Fernando Falceto
    [J]. Journal of Statistical Physics, 2010, 141 : 409 - 421
  • [9] AN ABSTRACT KAM THEOREM
    Garay, Mauricio
    [J]. MOSCOW MATHEMATICAL JOURNAL, 2014, 14 (04) : 745 - 772
  • [10] KAM theorem revisited
    Gentile, G
    Mastropietro, V
    [J]. PHYSICA D, 1996, 90 (03): : 225 - 234
12345