Fine Structures of Hyperbolic Diffeomorphisms

Alberto Pinto Awards& Honours: 2008 Recognition of the scientific merit of the works done in Psychology Sciences by the Psychology School of University of Minho 2007 Espinho Town hall Golden Medal by scientific merit 1984Prize Augusto Martins, University of Porto. 1981 One of the six winners of the Mini-Olympics of Mathematics in Portugal. David Rand Awards& Honours 1986 Whitehead Prize of the London Mathematical Society. 1988 Wolfson Research Award. 1988 Founding editor of Nonlinearity 2004 Fellow, Institute of Mathematics and Its Applications (by invitation) 2005 Britten Lecturer. McMaster University 2006 EPSRC Senior Research Fellowship

• HR structures.- Solenoid functions.- Self-renormalizable structures.- Rigidity.- Gibbs measures.- Measure scaling functions.- Measure solenoid functions.- Cocycle-gap pairs.- Hausdorff realizations.- Extended Livšic-Sinai eigenvalue formula.- Arc exchange systems and renormalization.- Golden tilings (in collaboration with J.P. Almeida and A. Portela).- Pseudo-Anosov diffeomorphisms in pseudo-surfaces.

From the reviews: "The book is a mostly self contained text on the theory of the fine scale structures of hyperbolic diffeomorphisms on surfaces. It is aimed at researchers and Ph. D students interested in the topic. Most of the text is based on the research work of the authors but it also contains related topics and background material. It is clearly written and very well structured." (Isabel Lugao Rios, Mathematical Reviews, Issue 2010 e) "The main theme of the book Fine Structures of Hyperbolic Diffeomorphisms, by Pinto, Rand and Ferreira, is the rigidity and flexibility of two-dimensional diffeomorphisms on hyperbolic basic sets and properties of invariant measures that are related to the geometry of these invariant sets. ... The book under review is based on a series of articles by the authors and is aimed at experts in the field. The theorems are clearly stated and complete proofs are provided." (W. De Melo, Bulletin of the American Mathematical Society, Vol. 48 (1), January, 2011)