TY  - GEN
AU  - Przytycki,Feliks
AU  - 
TI  - Conformal fractals: ergodic theory methods
T2  - London Mathematical Society lecture note series
SN  - 9780521438001
U1  - 514.742 
PY  - 2010///
CY  - Cambridge, New York
PB  - Cambridge University Press
KW  - Conformal geometry
KW  - Fractals
KW  - Ergodic theory
KW  - Iterative methods (Mathematics
N1  - Introduction -- 1. Basic examples and definitions 2. Measure-preserving endomorphisms -- 3. Ergodic theory on compact metric spaces -- 4. Distance-expanding maps -- 5. Thermodynamical formalism -- 6. Expanding repellers in manifolds and in the Riemann sphere: preliminaries -- 7. Cantor repellers in the line; Sullivan's scaling function; application in Feigenbaum universality -- 8. Fractal dimensions -- 9. Conformal expanding repellers -- 10. Sullivan's classification of conformal expanding repellers -- 11. Holomorphic maps with invariant probability measures of positive Lyapunov exponent -- 12. Conformal measures
N2  - "This is a one-stop introduction to the methods of ergodic theory applied to holomorphic iteration. The authors begin with introductory chapters presenting the necessary tools from ergodic theory thermodynamical formalism, and then focus on recent developments in the field of 1-dimensional holomorphic iterations and underlying fractal sets, from the point of view of geometric measure theory and rigidity. Detailed proofs are included. Developed from university courses taught by the authors, this book is ideal for graduate students. Researchers will also find it a valuable source of reference to a large and rapidly expanding field. It eases the reader into the subject and provides a vital springboard for those beginning their own research. Many helpful exercises are also included to aid understanding of the material presented and the authors provide links to further reading and related areas of research"--Provided by publisher
ER  -