Persistent Link:
http://hdl.handle.net/10150/186232
Title:
Dynamical systems and random perturbations.
Author:
Liu, Zheng.
Issue Date:
1993
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
This dissertation consists of two independent parts. In the first part we study the ergodic theory of surface endomorphisms. We consider non-uniformly expanding maps with generic singularities, and prove that the Pesin formula holds, which is to say that entropy is equal to the sum of the positive Lyapunov exponents if and only if the invariant probability measure in question is absolutely continuous with respect to Lebesgue measure. In the second part we study the small random perturbations of the Feigenbaum map related to the fixed point of Feigenbaum's renormalization operator for unimodal maps of the interval. We give a rigorous analysis of the changes in the geometry of the noisy attractor as noise level varies.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Dissertations, Academic.; Mathematics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Mathematics; Graduate College
Degree Grantor:
University of Arizona
Committee Chair:
Young, Lai-Sang

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleDynamical systems and random perturbations.en_US
dc.creatorLiu, Zheng.en_US
dc.contributor.authorLiu, Zheng.en_US
dc.date.issued1993en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThis dissertation consists of two independent parts. In the first part we study the ergodic theory of surface endomorphisms. We consider non-uniformly expanding maps with generic singularities, and prove that the Pesin formula holds, which is to say that entropy is equal to the sum of the positive Lyapunov exponents if and only if the invariant probability measure in question is absolutely continuous with respect to Lebesgue measure. In the second part we study the small random perturbations of the Feigenbaum map related to the fixed point of Feigenbaum's renormalization operator for unimodal maps of the interval. We give a rigorous analysis of the changes in the geometry of the noisy attractor as noise level varies.en_US
dc.description.notep. 75 missing from paper original and microfilm version.-
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectDissertations, Academic.en_US
dc.subjectMathematics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.chairYoung, Lai-Sangen_US
dc.contributor.committeememberWojtkowski, Maciejen_US
dc.contributor.committeememberRychlik, Mareken_US
dc.contributor.committeememberMaier, Roberten_US
dc.identifier.proquest9322762en_US
dc.identifier.oclc716272810en_US
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