Premium
Parabolic Rational Maps
Author(s) -
Haydn Nicolai,
Isola Stefano
Publication year - 2001
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1017/s0024610701001958
Subject(s) - mathematics , neighbourhood (mathematics) , jump , transformation (genetics) , dynamical systems theory , partition (number theory) , markov chain , operator (biology) , mathematical analysis , pure mathematics , statistical physics , combinatorics , physics , biochemistry , chemistry , statistics , repressor , quantum mechanics , transcription factor , gene
The paper studies the dynamics of rational maps with indifferent parabolic points by comparing their dynamical properties with those of their ‘jump transformation’ which is uniformly expanding on a non‐compact set with infinite Markov partition. It establishes the spectral properties of a two‐variables operator‐valued function associated to the jump transformation and exploits their dynamical relevance to allow the analytic properties of the pressure, the escape rate from a neighbourhood of the Julia set and the asymptotic distribution of pre‐images to be studied.