Dynamical systems and random perturbations.
| dc.contributor.author | Liu, Zheng. | |
| dc.creator | Liu, Zheng. | en_US |
| dc.date.accessioned | 2011-10-31T18:02:49Z | |
| dc.date.available | 2011-10-31T18:02:49Z | |
| dc.date.issued | 1993 | en_US |
| dc.identifier.uri | http://hdl.handle.net/10150/186232 | |
| dc.description.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. | |
| dc.language.iso | en | en_US |
| dc.publisher | The University of Arizona. | en_US |
| dc.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. | en_US |
| dc.subject | Dissertations, Academic. | en_US |
| dc.subject | Mathematics. | en_US |
| dc.title | Dynamical systems and random perturbations. | en_US |
| dc.type | text | en_US |
| dc.type | Dissertation-Reproduction (electronic) | en_US |
| dc.contributor.chair | Young, Lai-Sang | en_US |
| dc.identifier.oclc | 716272810 | en_US |
| thesis.degree.grantor | University of Arizona | en_US |
| thesis.degree.level | doctoral | en_US |
| dc.contributor.committeemember | Wojtkowski, Maciej | en_US |
| dc.contributor.committeemember | Rychlik, Marek | en_US |
| dc.contributor.committeemember | Maier, Robert | en_US |
| dc.identifier.proquest | 9322762 | en_US |
| thesis.degree.discipline | Mathematics | en_US |
| thesis.degree.discipline | Graduate College | en_US |
| thesis.degree.name | Ph.D. | en_US |
| dc.description.note | p. 75 missing from paper original and microfilm version. | |
| refterms.dateFOA | 2018-05-29T09:15:27Z | |
| html.description.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. |
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