Haydn, Nicolai Theodorus Antonius (1986) On dynamical systems. PhD thesis, University of Warwick.

Preview

Text WRAP_thesis_Haydn_1986.pdf - Submitted Version Download (5Mb) | Preview

Request Changes to record.

Abstract

Part A.
We prove existence of smooth invariant circles for area
preserving twist maps close enough to integrable using renormalisation. The
smoothness depends upon that of the map and the Liouville exponent of the
rotation number.

Part B.
Ruelle and Capocaccia gave a new definition of Gibbs states on
Smale spaces. Equilibrium
states of suitable function there on are known to be
Gibbs states. The converse in discussed in this paper, where the problem is
reduced to shift spaces and there solved by constructing suitable conjugating
homeomorphisms in order to verify the conditions for Gibbs states which
Bowen gave for shift spaces, where the equivalence to equilibrium states is
known.

Part C.
On subshifts which are derived from Markov partitions exists an
equivalence relation which idendifies points that lie on the boundary set of the
partition. In this paper we restrict to symbolic
dynamics. We express the
quotient space in terms of a non-transitive subshift of
finite type, give a
necessary and sufficient condition for the existence of a local product
structure and evaluate the Zeta function of the quotient space. Finally we give
an example where the quotient space is again a subshift of finite type.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Dynamics, Mathematics
Official Date:	June 1986
Dates:	Date Event June 1986 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	MacKay, Robert S., 1956- ; Walters, Peter, 1943-
Sponsors:	University of Warwick
Language:	eng

Request changes or add full text files to a record

Repository staff actions (login required)

View Item

Downloads