Bernhardt, Christopher Raymond (1980) Rotation numbers, periodic points and topological entropy of a class of endomorphisms of the circle. PhD thesis, University of Warwick.

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Abstract

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.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Topological entropy, Endomorphisms (Group theory), Topological dynamics
Official Date:	March 1980
Dates:	Date Event March 1980 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Rand, D. A. (David A.)
Sponsors:	Science Research Council (Great Britain)
Format of File:	pdf
Extent:	xi, 84 leaves
Language:	eng

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