Mestel, Benjamin David (1985) A computer assisted proof of universality for cubic critical maps of the circle with Golden Mean rotation number. PhD thesis, University of Warwick.

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Abstract

In order to explain the universal metric properties associated with
the breakdown of invariant tori in dissipative dynamical systems,
Ostlund, Rand, Sethna and Siggia together with Feigenbaum, Kadanoff
and Shenker have developed a renormalisation group analysis for
pairs of analytic functions that glue together to make a map of the
circle. Using a method of Lanford's, we have obtained a proof of the
existence and hyperbolicity of a non-trivial fixed point of the
renormalisation transformation for rotation number equal to the
golden mean (√5 - 1/2). The proof uses numerical estimates obtained
rigorously with the aid of a computer. These computer calculations
were based on a method of Eckmann, Koch and Wittwer.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Mappings (Mathematics), Dynamics, Golden section
Official Date:	September 1985
Dates:	Date Event September 1985 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Rand, David A.
Sponsors:	Science and Engineering Research Council (Great Britain) (SERC) ; Cornell University. Center for Applied Mathematics
Extent:	[7], 176 p.
Language:	eng

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