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: Computability of Julia Sets
  name:
    name part: Braverman, Mark.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Yampolsky, Michael.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2009
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIII, 151 p. online resource.
  abstract: Among all computer-generated mathematical images, Julia sets of rational maps occupy one of the most prominent positions. Their beauty and complexity can be fascinating. They also hold a deep mathematical content. Computational hardness of Julia sets is the main subject of this book. By definition, a computable set in the plane can be visualized on a computer screen with an arbitrarily high magnification. There are countless programs to draw Julia sets. Yet, as the authors have discovered, it is possible to constructively produce examples of quadratic polynomials, whose Julia sets are not computable. This result is striking - it says that while a dynamical system can be described numerically with an arbitrary precision, the picture of the dynamics cannot be visualized. The book summarizes the present knowledge about the computational properties of Julia sets in a self-contained way. It is accessible to experts and students with interest in theoretical computer science or dynamical systems.
  table of contents: to Computability -- Dynamics of Rational Mappings -- First Examples -- Positive Results -- Negative Results -- Computability versus Topological Properties of Julia Sets.
  note: by Mark Braverman, Michael Yampolsky.
  subject:
    topic: Mathematics
  subject:
    topic: Computer programming
  subject:
    topic: Computers
  subject:
    topic: Algorithms
  subject:
    topic: Computer science
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Mathematics
  subject:
    topic: Algorithms
  subject:
    topic: Algebra
  subject:
    topic: Programming Techniques
  subject:
    topic: Theory of Computation
  subject:
    topic: Algorithm Analysis and Problem Complexity
  subject:
    topic: Mathematics of Computing
  classification: QA76.9.A43
  classification: 518.1
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Algorithms and Computation in Mathematics, 23
  identifier: 9783540685470
  identifier: http://dx.doi.org/10.1007/978-3-540-68547-0
  record info:
    record creation date: 100301
    record change date: 20151204144144.0
    record identifier: 978-3-540-68547-0