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Some Problems in Unimodal Dynamics
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-7158-5865
1996 (English)Doctoral thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Royal Institute of Technology , 1996.
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-190804OAI: oai:DiVA.org:kth-190804DiVA: diva2:952944
Public defence
1996-12-16, D3, Lindstedtsvägen 5, Stockholm, 10:00 (English)
Opponent
Supervisors
Available from: 2016-08-18 Created: 2016-08-16 Last updated: 2016-08-18Bibliographically approved
List of papers
1. Absolutely continuous invariant measures and superstable periodic orbits: weak*-convergence of natural measures
Open this publication in new window or tab >>Absolutely continuous invariant measures and superstable periodic orbits: weak*-convergence of natural measures
1993 (English)Report (Other academic)
Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Royal Institute of Technology, 1993. 16 p.
Series
, TRITA-MAT, ISSN 0348-405X ; 93-0002
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:kth:diva-190171 (URN)
Note

QC 20160811

Available from: 2016-08-10 Created: 2016-08-10 Last updated: 2016-08-18Bibliographically approved
2. On Approach-Rate Conditions in Unimodal Dynamics
Open this publication in new window or tab >>On Approach-Rate Conditions in Unimodal Dynamics
(English)Manuscript (preprint) (Other academic)
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:kth:diva-190920 (URN)
External cooperation:
Note

Detta manuskript är en omarbetad version av den tidigare publicerade rapportenH. Thunberg, "Recurrence of the critical point," Stockholm, Department of Mathematics, Royal Institute of Technology, TRITA-MAT, 93-0034, 1993.

QC 20160826

Available from: 2016-08-18 Created: 2016-08-18 Last updated: 2016-08-26Bibliographically approved
3. Positive exponent in families with flat critical point
Open this publication in new window or tab >>Positive exponent in families with flat critical point
1999 (English)In: Ergodic Theory and Dynamical Systems, ISSN 0143-3857, E-ISSN 1469-4417, Vol. 19, no 3, 767-807 p.Article in journal (Refereed) Published
Abstract [en]

It is known that in generic, full unimodal families with a critical point of finite order, there exists a set of positive measure in parameter space such that the corresponding maps have chaotic behaviour. In this paper we prove the corresponding statement for certain families of unimodal maps with flat critical point. One of the key-points is a large deviation argument for sums of ‘almost’ independent random variables with only finitely many moments.

Place, publisher, year, edition, pages
Cambridge University Press, 1999
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:kth:diva-190144 (URN)000081037700015 ()2-s2.0-0033457439 (ScopusID)
Note

QC 20160811

Available from: 2016-08-10 Created: 2016-08-10 Last updated: 2016-08-18Bibliographically approved
4. A recycled characterization of kneading sequences
Open this publication in new window or tab >>A recycled characterization of kneading sequences
1999 (English)In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, ISSN 0218-1274, Vol. 9, no 9, 1883-1887 p.Article in journal (Refereed) Published
Abstract [en]

For any infinite sequence E on two symbols one can define two sequences of positive integers S(E) (the splitting times) and T(E) (the cosplitting times), which each describe the self-replicative structure of E. If E is the kneading sequence of a unimodal map, it is known that S(E) and T(E) carry a lot of information on the dynamics, and that they are disjoint. We show the reverse implication: A nonperiodic sequence E is the kneading sequence of some unimodal map if the sequences S(E) and T(E) are disjoint.

Place, publisher, year, edition, pages
World Scientific, 1999
Keyword
Unimodal dynamical systems, kneading theory
National Category
Other Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kth:diva-190142 (URN)10.1142/S0218127499001371 (DOI)000083733300021 ()
Note

QC 20160810

Available from: 2016-08-10 Created: 2016-08-10 Last updated: 2016-08-18Bibliographically approved

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