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Renormalization for Siegel discs

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thesis
posted on 22.12.2017, 11:40 by Andrew D. Burbanks
This thesis investigates the existence of Siegel discs for iterated complex maps and looks at the properties of their boundary curves for golden mean rotation number. The key tool used is the idea of a renormalization operator acting on a space of functions. Firstly, a computer-assisted proof is discussed and verified, which establishes the existence of a fixed point of the relevant renormalization operator. In particular, the proof yields a ball of functions around an approximate fixed point that is guaranteed to contain the true fixed point. [Continues.]

Funding

Loughborough University (studentship). Loughborough University, Department of Mathematical Sciences. EPSRC (studentship no. 94001339).

History

School

  • Science

Department

  • Mathematical Sciences

Publisher

© Andrew D. Burbanks

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 2.5 Generic (CC BY-NC-ND 2.5) licence. Full details of this licence are available at: http://creativecommons.org/licenses/by-nc-nd/2.5/

Publication date

1997

Notes

A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.

Language

en

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