Coverart for item
The Resource Distance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry, Volker Mayer, Bartlomiej Skorulski, Mariusz Urbanski

Distance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry, Volker Mayer, Bartlomiej Skorulski, Mariusz Urbanski

Label
Distance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry
Title
Distance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry
Statement of responsibility
Volker Mayer, Bartlomiej Skorulski, Mariusz Urbanski
Creator
Contributor
Subject
Language
eng
Summary
Annotation The theory of random dynamical systems originated from stochasticdifferential equations. It is intended to provide a framework andtechniques to describe and analyze the evolution of dynamicalsystems when the input and output data are known only approximately, according to some probability distribution. The development of this field, in both the theory and applications, has gone in many directions. In this manuscript we introduce measurable expanding random dynamical systems, develop the thermodynamical formalism and establish, in particular, the exponential decay of correlations and analyticity of the expected pressure although the spectral gap property does not hold. This theory is then used to investigate fractal properties of conformal random systems. We prove a Bowens formula and develop the multifractal formalism of the Gibbs states. Depending on the behavior of the Birkhoff sums of the pressure function we arrive at a natural classification of the systems into two classes: quasi-deterministic systems, which share manyproperties of deterministic ones; and essentially random systems, which are rather generic and never bi-Lipschitz equivalent to deterministic systems. We show that in the essentially random case the Hausdorff measure vanishes, which refutes a conjecture by Bogenschutz and Ochs. Lastly, we present applications of our results to various specific conformal random systems and positively answer a question posed by Bruck and Buger concerning the Hausdorff dimension of quadratic random Julia sets
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorDate
1964-
http://library.link/vocab/creatorName
Mayer, Volker
Dewey number
515/.39
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA614.835
LC item number
.M39 2011
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
  • Skorulski, Bartlomiej
  • Urbański, Mariusz
Series statement
Lecture notes in mathematics,
Series volume
2036
http://library.link/vocab/subjectName
  • Random dynamical systems
  • Fractals
  • Fractals
  • Random dynamical systems
Label
Distance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry, Volker Mayer, Bartlomiej Skorulski, Mariusz Urbanski
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 109-110) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
1 Introduction -- 2 Expanding Random Maps -- 3 The RPF-theorem -- 4 Measurability, Pressure and Gibbs Condition -- 5 Fractal Structure of Conformal Expanding Random Repellers -- 6 Multifractal Analysis -- 7 Expanding in the Mean -- 8 Classical Expanding Random Systems -- 9 Real Analyticity of Pressure
Control code
759858108
Dimensions
unknown
Extent
1 online resource (x, 112 pages)
File format
unknown
Form of item
online
Isbn
9783642236501
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-642-23650-1
Other physical details
illustrations (some color).
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)759858108
Label
Distance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry, Volker Mayer, Bartlomiej Skorulski, Mariusz Urbanski
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 109-110) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
1 Introduction -- 2 Expanding Random Maps -- 3 The RPF-theorem -- 4 Measurability, Pressure and Gibbs Condition -- 5 Fractal Structure of Conformal Expanding Random Repellers -- 6 Multifractal Analysis -- 7 Expanding in the Mean -- 8 Classical Expanding Random Systems -- 9 Real Analyticity of Pressure
Control code
759858108
Dimensions
unknown
Extent
1 online resource (x, 112 pages)
File format
unknown
Form of item
online
Isbn
9783642236501
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-642-23650-1
Other physical details
illustrations (some color).
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)759858108

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