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Combinatorial dynamics on the interval and a generalization of Sharkovskiĭ's theorem
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Kuchta, Milan (1994) Combinatorial dynamics on the interval and a generalization of Sharkovskiĭ's theorem. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3216372~S15
Abstract
We study the discrete one dimensional dynamical systems given by continuous functions mapping a closed real interval into itself and the law of coexistence of periodic orbits for such systems.
In chapter 1 we study invariant measures for a continuous function which maps a real interval into itself. We show that the ratio of the measures of the two subintervals into which it is divided by a fixed point is constrained by the set of periods of periodic points. As a consequence of this we get new information about the law of coexistence of periodic orbits.
In chapter 2 we study the law of coexistence of different types of periodic orbits more closely. Based on the idea from chapter 1 we introduce the term eccentricity of a periodic orbit and study the coexistence law between periodic orbits with different eccentricities. We also characterize those periodic orbits with a given eccentricity that are simplest from the point of view of the coexistence law. We obtain a generalization of Sharkovskii's Theorem where the notion of period of periodic orbit is replaced by the notion of eccentricity of periodic orbit.
Chapter 2 is independent of chapter 1 but uses ideas that originated in the work covered by chapter 1.
| Item Type: | Thesis (PhD) | ||||
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| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Combinatorial dynamics, Functions, Continuous | ||||
| Official Date: | 1994 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Mathematics Institute | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Manning, Anthony, 1946- | ||||
| Sponsors: | University of Warwick ; Council of Vice Chancellors and Principals | ||||
| Extent: | v, 54 leaves : charts | ||||
| Language: | eng |
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