Details of Grant 

EPSRC Reference:	GR/S00590/01
Title:	generalized pseudo-anosovs and piecewise linear models in two-dimensional dynamics
Principal Investigator:	Hall, Dr T
Other Investigators:
Researcher Co-Investigators:
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Department:	Mathematical Sciences
Organisation:	University of Liverpool
Scheme:	Standard Research (Pre-FEC)
Starts:	22 July 2002	Ends:	21 October 2002	Value (£):	5,859
EPSRC Research Topic Classifications:	Algebra & Geometry Mathematical Analysis
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
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Panel History:
Summary on Grant Application Form
Describe the proposed research in about 200 words.The long term goal of the proposed research is to construct piecewise linear models for surface diffeomorphisms and to use them to study the dynamics of families of such diffeomorphisms (such as the Henon family).The first steps towards this goal consist of defining an appropriate notion of convergence for pseudo-Anosov and generalized pseudo-Anosov maps, and to complete countable families of such maps arising from the study of horseshoe braid forcing.The techniques proposed bring together Thurston's classification of surface homeomorphisms, conformal and quasi-conformal mappings, continuity properties of transfer operators, and the dynamics of unimodal maps.
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Organisation Website:	http://www.liv.ac.uk