Ergodic theory and fractal geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Soc.
2014
|
| Series: | CBMS regional conference series in mathematics
120 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | IX, 69 S. Ill., graph. Darst. |
| ISBN: | 9781470410346 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
ix
Chapter
1.
Introduction to Fractals
1
Chapter
2.
Dimension
11
Chapter
3.
Trees and Fractals
15
Chapter
4.
Invariant Sets
21
Chapter
5.
Probability Trees
23
Chapter
6.
Galleries
27
Chapter
7.
Probability Trees Revisited
31
Chapter
8.
Elements of Ergodic Theory
33
Chapter
9.
Galleries of Trees
35
Chapter
10.
General Remarks on Markov Systems
37
Chapter
11.
Markov Operator
Τ
and Measure Preserving Transformation
Τ
39
Chapter
12.
Probability Trees and Galleries
43
Chapter
13.
Ergodic Theorem and the Proof of the Main Theorem
47
Chapter
14.
An Application: The
/с
-lane
property ol
Chapter
15.
Dimension and Energy
53
Chapter
.1.6.
Dimension Conservation
55
Chapter
17.
Ergodic Theorem for Sequences of Functions
57
Chapter
18.
Dimension Conservation for Homogeneous Fractals: The Main
Steps in the Proof
59
Chapter
19.
Verifying the Conditions of the Ergodic Theorem for Sequences
of Functions
65
Bibliography
67
Index
69
Fractal
geometry
represents a radical departure from classical geometry, which
focuses on smooth objects that straighten out under magnification. Fractals,
which take their name from the shape of fractured objects, can be character¬
ized as retaining their lack of smoothness under magnification. The properties of
fractals come to light under repeated magnification, which we refer to informally
as zooming in . This zooming-in process has its parallels in dynamics, and the
varying scenery corresponds to the evolution of dynamical variables.
The present monograph focuses on applications of one branch of dynamics
—
ergodic theory
—
to the geometry of fractals. Much attention is given to the
all-important notion of fractal dimension, which is shown to be intimately related
to the study of ergodic averages. It has been long known that dynamical systems
serve as a rich source of fractal examples. The primary goal in this monograph is to
demonstrate how the minute structure of fractals is unfolded when seen in the light
of related dynamics.
|
| any_adam_object | 1 |
| author | Furstenberg, Harry 1935- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.48 |
| dewey-search | 515/.48 |
| dewey-sort | 3515 248 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV042140261 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:13:41Z |
| institution | BVB |
| isbn | 9781470410346 |
| language | English |
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| physical | IX, 69 S. Ill., graph. Darst. |
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| publisher | American Mathematical Soc. |
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| spelling | Furstenberg, Harry 1935- Verfasser (DE-588)1060419742 aut Ergodic theory and fractal geometry Hillel Furstenberg Providence, R.I. American Mathematical Soc. 2014 IX, 69 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier CBMS regional conference series in mathematics 120 Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Fraktalgeometrie (DE-588)4473576-5 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2011 Kent, Ohio gnd-content Ergodentheorie (DE-588)4015246-7 s Fraktalgeometrie (DE-588)4473576-5 s DE-604 CBMS regional conference series in mathematics 120 (DE-604)BV000004346 120 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027580243&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027580243&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Furstenberg, Harry 1935- Ergodic theory and fractal geometry CBMS regional conference series in mathematics Ergodentheorie (DE-588)4015246-7 gnd Fraktalgeometrie (DE-588)4473576-5 gnd |
| subject_GND | (DE-588)4015246-7 (DE-588)4473576-5 (DE-588)1071861417 |
| title | Ergodic theory and fractal geometry |
| title_auth | Ergodic theory and fractal geometry |
| title_exact_search | Ergodic theory and fractal geometry |
| title_full | Ergodic theory and fractal geometry Hillel Furstenberg |
| title_fullStr | Ergodic theory and fractal geometry Hillel Furstenberg |
| title_full_unstemmed | Ergodic theory and fractal geometry Hillel Furstenberg |
| title_short | Ergodic theory and fractal geometry |
| title_sort | ergodic theory and fractal geometry |
| topic | Ergodentheorie (DE-588)4015246-7 gnd Fraktalgeometrie (DE-588)4473576-5 gnd |
| topic_facet | Ergodentheorie Fraktalgeometrie Konferenzschrift 2011 Kent, Ohio |
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