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Domain of analyticity of normalizing transformations
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2006 (English)In: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 19, no 7, 1581-1599 p.Article in journal (Refereed) Published
Abstract [en]

We investigate questions of divergence or local convergence of (formal) normalizing transformations associated with the Birkhoff normal form (BNF) at the origin of a holomorphic Hamiltonian system. These questions are addressed for systems for which the BNF is a quadratic function H-Lambda = Sigma(d)(j=1) lambda(j) x(j) y(j), Lambda := (lambda(1),..., lambda(d)) being a non-resonant, either real or purely imaginary, vector. We prove that for a generic Lambda is an element of R-d or i Lambda is an element of R-d one can define Hamiltonians H = H-Lambda + (H) over cap satisfying the following properties: (i) H is real-analytic, holomorphic in the unit polydisc D(1), and H is defined arbitrarily close to H-Lambda, (ii) the BNF of H equals H-Lambda and (iii) any symplectic normalizing transformation diverges, or given any 0 < rho < 1 any normalizing transformation diverges outside the polydisc of radius rho, and there is a real-analytic normalizing transformation (converging in a smaller domain).

Place, publisher, year, edition, pages
2006. Vol. 19, no 7, 1581-1599 p.
Keyword [en]
ANALYTISCHER HAMILTONSCHER DIFFERENTIALGLEICHUNGEN, NAHE EINER GLEICHGEWICHTSLOSUNG, NORMAL FORMS, CONVERGENCE, SYSTEMS
National Category
Computational Mathematics Other Physics Topics
Identifiers
URN: urn:nbn:se:kth:diva-13919DOI: 10.1088/0951-7715/19/7/007ISI: 000238372600007OAI: oai:DiVA.org:kth-13919DiVA: diva2:328241
Note
QC 20100702Available from: 2010-07-02 Created: 2010-07-02 Last updated: 2010-07-15Bibliographically approved
In thesis
1. Non-linearizability, unique ergodicity and weak mixing in dynamics
Open this publication in new window or tab >>Non-linearizability, unique ergodicity and weak mixing in dynamics
2003 (English)Doctoral thesis, comprehensive summary (Other scientific)
Place, publisher, year, edition, pages
Stockholm: KTH, 2003. xvii p.
Series
Trita-MAT. MA, ISSN 1401-2278 ; 2003:05
Keyword
Ergodicity, weak mixing, Hamiltonian systems
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-3610 (URN)91-7283-585-0 (ISBN)
Public defence
2003-10-06, 00:00
Note
QC 20100702Available from: 2003-10-01 Created: 2003-10-01 Last updated: 2010-07-02Bibliographically approved

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