Dynamical systems: examples of complex behaviour
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2005
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 181 - 183 Auch als Internetausgabe |
| Beschreibung: | VIII, 189 S. graph. Darst. |
| ISBN: | 3540229086 9783540229087 |
Internformat
MARC
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|---|---|---|---|
| 001 | BV020020625 | ||
| 003 | DE-604 | ||
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| 015 | |a 05,N09,0639 |2 dnb | ||
| 016 | 7 | |a 973646993 |2 DE-101 | |
| 020 | |a 3540229086 |c Pb. : ca. EUR 40.02 (freier Pr.), ca. sfr 68.50 (freier Pr.) |9 3-540-22908-6 | ||
| 020 | |a 9783540229087 |9 978-3-540-22908-7 | ||
| 024 | 3 | |a 9783540229087 | |
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| 100 | 1 | |a Jost, Jürgen |d 1956- |e Verfasser |0 (DE-588)115774564 |4 aut | |
| 245 | 1 | 0 | |a Dynamical systems |b examples of complex behaviour |c Jürgen Jost |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2005 | |
| 300 | |a VIII, 189 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Universitext | |
| 500 | |a Literaturverz. S. 181 - 183 | ||
| 500 | |a Auch als Internetausgabe | ||
| 650 | 4 | |a Dynamique différentiable | |
| 650 | 7 | |a Dynamische systemen |2 gtt | |
| 650 | 7 | |a Equações diferenciais |2 larpcal | |
| 650 | 7 | |a Sistemas dinâmicos |2 larpcal | |
| 650 | 7 | |a Teoria qualitativa |2 larpcal | |
| 650 | 4 | |a Chaotic behavior in systems | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Differential equations |x Qualitative theory | |
| 650 | 0 | 7 | |a Dynamisches System |0 (DE-588)4013396-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Dynamisches System |0 (DE-588)4013396-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013341999&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-013341999 | ||
Datensatz im Suchindex
| _version_ | 1804133582309949440 |
|---|---|
| adam_text | Table
of
Contents
Introduction
.............................................. 1
Stability of dynamical systems, bifurcations, and generic
properties
................................................ 7
2.1
Some general notions
................................... 7
2.2
Autonomous systems of ODEs
........................... 9
2.3
Examples: Bifurcation depending on a parameter
λ
Є
R.....
15
2.4
Chaos in differential and difference equations. The concept
of an attractor
......................................... 22
2.5
Interaction, or the interplay between concentration or
reaction and diffusion
................................... 36
2.6
Discrete and continuous systems. The
Poincaré
return map
. 41
2.7
Stability and bifurcations; generic properties
............... 42
2.8
The
Hopf
bifurcation
................................... 46
2.9
Lotka-
Volterra equations
................................ 48
2.10
Stable, unstable, and center manifolds
..................... 52
Discrete invariants of dynamical systems
................. 61
3.1
The topology of graphs
.................................. 61
3.2
Floer homology
........................................ 62
3.3
Conley theory: examples and results
...................... 70
3.4
Cohomological Conley index
............................. 77
3.5
Homotopical invariants
.................................. 80
3.6
Continuation properties of the Conley index
............... 92
3.7
The discrete Conley index
............................... 93
Entropy and topological aspects of dynamical systems
.... 99
4.1
The entropy of a process as an asymptotic quantity
........ 99
4.2
Positive entropy and chaos
............................... 103
4.3
Symbolic dynamics
..................................... 108
Entropy and metric aspects of dynamical systems
........
Ill
5.1
The metric approach to topological entropy
................
Ill
5.2
Complexity and intrinsic scales
........................... 114
6
Entropy and measure theoretic aspects of dynamical
systems
................................................... 119
6.1
Probability spaces and measure preserving maps
............ 119
6.2
Ergodicity
............................................ 121
6.3
Entropy and information
................................ 126
6.4
Invariant measures
..................................... 138
6.5
Stochastic processes
.................................... 142
6.6
Stochastic bifurcations
.................................. 149
7
Smooth dynamical systems
............................... 153
7.1
Lyapunov exponents
................................... 153
7.2
Hyperbolicity
.......................................... 156
7.3
Information loss
........................................ 165
8
Cellular automata and Boolean networks as examples of
discrete dynamical systems
............................... 169
8.1
Cellular automata
...................................... 169
8.2
Boolean networks
....................................... 175
References
.................................................... 181
Index
......................................................... 185
|
| any_adam_object | 1 |
| author | Jost, Jürgen 1956- |
| author_GND | (DE-588)115774564 |
| author_facet | Jost, Jürgen 1956- |
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| bvnumber | BV020020625 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 810 SK 520 |
| classification_tum | MAT 344f |
| ctrlnum | (OCoLC)61263422 (DE-599)BVBBV020020625 |
| dewey-full | 515/.39 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.39 |
| dewey-search | 515/.39 |
| dewey-sort | 3515 239 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T20:11:00Z |
| institution | BVB |
| isbn | 3540229086 9783540229087 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013341999 |
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| physical | VIII, 189 S. graph. Darst. |
| publishDate | 2005 |
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| publisher | Springer |
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| spelling | Jost, Jürgen 1956- Verfasser (DE-588)115774564 aut Dynamical systems examples of complex behaviour Jürgen Jost Berlin [u.a.] Springer 2005 VIII, 189 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Literaturverz. S. 181 - 183 Auch als Internetausgabe Dynamique différentiable Dynamische systemen gtt Equações diferenciais larpcal Sistemas dinâmicos larpcal Teoria qualitativa larpcal Chaotic behavior in systems Differentiable dynamical systems Differential equations Qualitative theory Dynamisches System (DE-588)4013396-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s DE-604 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013341999&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jost, Jürgen 1956- Dynamical systems examples of complex behaviour Dynamique différentiable Dynamische systemen gtt Equações diferenciais larpcal Sistemas dinâmicos larpcal Teoria qualitativa larpcal Chaotic behavior in systems Differentiable dynamical systems Differential equations Qualitative theory Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4013396-5 |
| title | Dynamical systems examples of complex behaviour |
| title_auth | Dynamical systems examples of complex behaviour |
| title_exact_search | Dynamical systems examples of complex behaviour |
| title_full | Dynamical systems examples of complex behaviour Jürgen Jost |
| title_fullStr | Dynamical systems examples of complex behaviour Jürgen Jost |
| title_full_unstemmed | Dynamical systems examples of complex behaviour Jürgen Jost |
| title_short | Dynamical systems |
| title_sort | dynamical systems examples of complex behaviour |
| title_sub | examples of complex behaviour |
| topic | Dynamique différentiable Dynamische systemen gtt Equações diferenciais larpcal Sistemas dinâmicos larpcal Teoria qualitativa larpcal Chaotic behavior in systems Differentiable dynamical systems Differential equations Qualitative theory Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Dynamique différentiable Dynamische systemen Equações diferenciais Sistemas dinâmicos Teoria qualitativa Chaotic behavior in systems Differentiable dynamical systems Differential equations Qualitative theory Dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013341999&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT jostjurgen dynamicalsystemsexamplesofcomplexbehaviour |