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Title: Rotation numbers, periodic points and topological entropy of a class of endomorphisms of the circle
Author: Bernhardt, Christopher Raymond
ISNI:       0000 0001 3461 6063
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1980
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In this thesis we consider the dynamics of a class of endomorphisms of the circle, we denote this class of functions by Λ. Following the work of Milnor and Thurston [6] we develop a kneading theory for these functions, which enables us to calculate the entropy of our maps and to show that entropy is continuous. We then show that any map, f ε Λ, with positive entropy is topologically semi-conjugate to a piecewise linear map, F. The map F is determined by two real numbers, the topological entropy of f and the twist number of f, both of which can be calculated from the kneading matrix. Using the fact that the rotation intervals of f and F are the same, we give a method of calculating this interval from the twist number and entropy of f. The final chapter is motivated by a theorem of Sarkovskii [9] and concerns universal properties of the periodic points.
Supervisor: Not available Sponsor: Science Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics