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Title: Combinatorial dynamics on the interval and a generalization of Sharkovskii's Theorem
Author: Kuchta, Milan
ISNI:       0000 0001 3602 7342
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1994
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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.
Supervisor: Not available Sponsor: University of Warwick ; Council of Vice Chancellors and Principals
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics