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
Resource Information
The item Distance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry, Volker Mayer, Bartlomiej Skorulski, Mariusz Urbanski represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Distance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry, Volker Mayer, Bartlomiej Skorulski, Mariusz Urbanski represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 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: quasideterministic systems, which share manyproperties of deterministic ones; and essentially random systems, which are rather generic and never biLipschitz 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
 Language
 eng
 Extent
 1 online resource (x, 112 pages)
 Contents

 1 Introduction
 2 Expanding Random Maps
 3 The RPFtheorem
 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
 Isbn
 9783642236501
 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
 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: quasideterministic systems, which share manyproperties of deterministic ones; and essentially random systems, which are rather generic and never biLipschitz 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
 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
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references (pages 109110) 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 RPFtheorem  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
 10.1007/9783642236501
 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
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references (pages 109110) 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 RPFtheorem  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
 10.1007/9783642236501
 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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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Distanceexpandingrandommappings/7yPgW9KprUA/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Distanceexpandingrandommappings/7yPgW9KprUA/">Distance expanding random mappings, thermodynamical formalism, Gibbs measures and fractal geometry, Volker Mayer, Bartlomiej Skorulski, Mariusz Urbanski</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>