rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Open Conformal Systems and Perturbations of Transfer Operators
  name:
    name part: Pollicott, Mark.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Urbański, Mariusz.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2017
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XII, 204 p. online resource.
  abstract: The focus of this book is on open conformal dynamical systems corresponding to the escape of a point through an open Euclidean ball. The ultimate goal is to understand the asymptotic behavior of the escape rate as the radius of the ball tends to zero. In the case of hyperbolic conformal systems this has been addressed by various authors. The conformal maps considered in this book are far more general, and the analysis correspondingly more involved. The asymptotic existence of escape rates is proved and they are calculated in the context of (finite or infinite) countable alphabets, uniformly contracting conformal graph-directed Markov systems, and in particular, conformal countable alphabet iterated function systems. These results have direct applications to interval maps, meromorphic maps and rational functions. Towards this goal the authors develop, on a purely symbolic level, a theory of singular perturbations of Perron--Frobenius (transfer) operators associated with countable alphabet subshifts of finite type and Hölder continuous summable potentials. This leads to a fairly full account of the structure of the corresponding open dynamical systems and their associated surviving sets.
  table of contents: 1. Introduction -- 2. Singular Perturbations of Classical Original Perron–Frobenius Operators on Countable Alphabet Symbol Spaces -- 3. Symbol Escape Rates and the Survivor Set K(Un) -- 4. Escape Rates for Conformal GDMSs and IFSs -- 5. Applications: Escape Rates for Multimodal Maps and One-Dimensional Complex Dynamics.
  note: by Mark Pollicott, Mariusz Urbański.
  subject:
    topic: Mathematics
  subject:
    topic: Dynamics
  subject:
    topic: Ergodic theory
  subject:
    topic: Functional analysis
  subject:
    topic: Functions of complex variables
  subject:
    topic: Measure theory
  subject:
    topic: Operator theory
  subject:
    topic: Mathematics
  subject:
    topic: Dynamical Systems and Ergodic Theory
  subject:
    topic: Functional Analysis
  subject:
    topic: Functions of a Complex Variable
  subject:
    topic: Operator Theory
  subject:
    topic: Measure and Integration
  classification: QA313
  classification: 515.39
  classification: 515.48
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes in Mathematics, 2206
  identifier: 9783319721798
  identifier: http://dx.doi.org/10.1007/978-3-319-72179-8
  record info:
    record creation date: 180206
    record change date: 20180206192915.0
    record identifier: 978-3-319-72179-8