Denvir, James (1994) Two topics in dynamics. PhD thesis, University of Warwick.

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Abstract

This thesis consists of two independent chapters. Both present results in the field of dynamical systems.

In the first chapter we study abstract adding machines and their occurrence in unimodal maps of the interval. For unimodal maps with no aperiodic homtervals we characterize completely when adding machines occur. We also discuss their importance in relation to the boundary of positive topological entropy for two-parameter families of diffeomorphisms of the disc.

In the second chapter we prove existence of a distinguished set of geodesics on orientable Riemannian surfaces with geodesic boundary and negative Euler characteristic. This result allows us to construct a semi-equivalence between a subset of the unit tangent bundle of the surface with the arbitrary Riemannian metric and the unit tangent bundle given by the standard hyperbolic metric on this surface. The result is analogous to one of Morse [Ml] for surfaces without boundary. We give a new proof of Morse’s result using a method similar to the proof of our new result.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Dynamics, Topological entropy, Diffeomorphisms, Geometry, Riemannian, Geodesics (Mathematics)
Official Date:	1994
Dates:	Date Event 1994 UNSPECIFIED
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	MacKay, Robert S. 1956-
Sponsors:	Science and Engineering Research Council (Great Britain) ; University of Warwick
Extent:	iii, 49 leaves : illustrations
Language:	eng

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