Details of Grant 

EPSRC Reference:	GR/R54477/01
Title:	The mixing propoerties of dissipative partially hyperbolic dynamical systems and the fine structure of measures in non-uniformly hyperbolic systems
Principal Investigator:	Nicol, Professor M
Other Investigators:	Stratmann, Dr B Sharp, Professor R
Researcher Co-Investigators:
Project Partners:
Department:	Sch of Electronics & Physical Sciences
Organisation:	University of Surrey
Scheme:	Standard Research (Pre-FEC)
Starts:	01 May 2002	Ends:	31 July 2002	Value (£):	13,403
EPSRC Research Topic Classifications:	Mathematical Analysis
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:
Summary on Grant Application Form
A good understanding of the mixing properties of both conservative and dissipative chaotic systems is necessary to explain such physically relevant properties of chaotic systems as random-walk like behaviour, decay of correlations, and the extent to which future states of the system may be predicted . Only a small class of models for chaotic behaviour are well-understood - in particular the theory concerning uniformly hyperbolic systems is well developed. Remarkable progress has recently been made on extending a quantitative understanding of mixing behaviour from uniformly hyperbolic systems to partially hyperbolic systems. Partially hyperbolic systems occur frequently in applications, especially in systems with symmetry. Unfortunately this recent progress has been limited to systems which are conservative. We propose to extend this understanding to the important context of dissipative systems. This will require a precise undertanding of the fractal properties and fine structure of invariant measures in partially hyperbolic systems. In related work we will investigate the fractal structure of invariant sets and measures in random dynamical systems (iterated function systems) which contract non-uniformly. These systems are used widely in data compression and models for randomly perturbed systems. So far results have been (mainly) limited to the case of uniform contraction. We will extend our understanding to the case of non-uniform contraction.
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