Domain of analyticity of normalizing transformations
2006 (English)In: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 19, no 7, 1581-1599 p.Article in journal (Refereed) Published
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.
ANALYTISCHER HAMILTONSCHER DIFFERENTIALGLEICHUNGEN, NAHE EINER GLEICHGEWICHTSLOSUNG, NORMAL FORMS, CONVERGENCE, SYSTEMS
Computational Mathematics Other Physics Topics
IdentifiersURN: urn:nbn:se:kth:diva-13919DOI: 10.1088/0951-7715/19/7/007ISI: 000238372600007OAI: oai:DiVA.org:kth-13919DiVA: diva2:328241
QC 201007022010-07-022010-07-022010-07-15Bibliographically approved