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Non-linearizability, unique ergodicity and weak mixing in dynamics
KTH, Superseded Departments, Mathematics.
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 [en]
Ergodicity, weak mixing, Hamiltonian systems
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-3610ISBN: 91-7283-585-0 (print)OAI: oai:DiVA.org:kth-3610DiVA: diva2:9440
Public defence
2003-10-06, 00:00
Note
QC 20100702Available from: 2003-10-01 Created: 2003-10-01 Last updated: 2010-07-02Bibliographically approved
List of papers
1. Analytic nonlinearizable uniquely ergodic diffeomorphisms on T-2
Open this publication in new window or tab >>Analytic nonlinearizable uniquely ergodic diffeomorphisms on T-2
2003 (English)In: Ergodic Theory and Dynamical Systems, ISSN 0143-3857, E-ISSN 1469-4417, Vol. 23, 935-955 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we study the behavior of diffeomorphisms, contained in the closure (A) over bar (alpha) (in the inductive limit topology) of the set A(alpha) of real-analytic diffeomorphisms of the torus T-2, which are conjugated to the rotation R-alpha : (x, y) hooked right arrow (x+alpha, y) by an analytic measure-preserving transformation. We show that for a generic alpha is an element of [0, 1], (A) over bar (alpha) contains a dense set of uniquely ergodic diffeomorphisms. We also prove that (A) over bar (alpha) contains a dense set of diffeomorphisms that are minimal and non-ergodic.

Keyword
FLOWS, TORUS
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-13920 (URN)10.1017/S0143385702001542 (DOI)000184382900015 ()
Note
QC 20100702Available from: 2010-07-02 Created: 2010-07-02 Last updated: 2017-12-12Bibliographically approved
2. Weakly mixing diffeomorphisms on the torus, annulus and disc
Open this publication in new window or tab >>Weakly mixing diffeomorphisms on the torus, annulus and disc
(English)Article in journal (Other academic) Submitted
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-13918 (URN)
Note
QS 2012Available from: 2010-07-02 Created: 2010-07-02 Last updated: 2012-03-28Bibliographically approved
3. Domain of analyticity of normalizing transformations
Open this publication in new window or tab >>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
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).

Keyword
ANALYTISCHER HAMILTONSCHER DIFFERENTIALGLEICHUNGEN, NAHE EINER GLEICHGEWICHTSLOSUNG, NORMAL FORMS, CONVERGENCE, SYSTEMS
National Category
Computational Mathematics Other Physics Topics
Identifiers
urn:nbn:se:kth:diva-13919 (URN)10.1088/0951-7715/19/7/007 (DOI)000238372600007 ()
Note
QC 20100702Available from: 2010-07-02 Created: 2010-07-02 Last updated: 2017-12-12Bibliographically approved

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Citation style
  • apa
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More styles
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  • Other locale
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Output format
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