Verfügbarkeit: Aspects of ergodic, qualitative and statistical theory of motion

Aspects of ergodic, qualitative and statistical theory of motion:

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Bibliographische Detailangaben
Beteiligte Personen:	Gallavotti, Giovanni (VerfasserIn), Bonetto, Federico (VerfasserIn), Gentile, Guido (VerfasserIn)
Format:	Buch
Sprache:	Englisch Italienisch
Veröffentlicht:	Berlin Springer 2004
Schriftenreihe:	Texts and monographs in physics
Schlagwörter:	Dynamique différentiable Ergodiciteit Mecânica estatística Mécanique statistique Sistemas dinâmicos diferenciáveis Statistische mechanica Teoria ergodica Théorie ergodique Transformations conservant la mesure Differentiable dynamical systems Ergodic theory Measure-preserving transformations Statistical mechanics Statistische Mechanik Ergodentheorie
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010537589&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	X, 435 S. graph. Darst.
ISBN:	3540408797 9783540408796

Internformat

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Datensatz im Suchindex

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adam_text	G. GENTILE G. GALLAVOTTI F. BONETTO ASPECTS OF ERGODIC, QUALITATIVE AND STATISTICAL THEORY OF MOTION WITH 38 FIGURES SPRINGER CONTENTS 1 GENERAL QUALITATIVE PROPERTIES ........................... 1 1.1 HISTORICAL NOTE ......................................... 1 1.2 EXAMPLES AND SOME DEFINITIONS .......................... 3 1.3 AS DYNAMICAL SYSTEMS ............... ................ 13 1.4 FREQUENCIES OF VISIT .................. ................ 17 2 ERGODICITY AND ERGODIC POINTS ............................ 27 HARMONIC OSCILLATORS AND INTEGRABLE SYSTEMS 2.1 QUASI-PERIODIC MOTIONS AND INTEGRABILITY ............... 27 2.2 ERGODIC PROPERTIES OF QUASI-PERIODIC MOTIONS . ERGODIC SEQUENCES AND MEASURES ....... ............... 32 2.3 ERGODIC POINTS ............................ ......... 52 2.4 ERGODIC DECOMPOSITION .................................. 62 3 ENTROPY AND COMPLEXITY .................................. 73 3.1 COMPLEXITY OF MOTIONS AND ENTROPY ...................... 73 3.2 THE SHANNON-MCMILLAN THEOREM ......................... 81 3.3 ELEMENTARY PROPERTIES OF THE AVERAGE ENTROPY ............. 92 3.4 FURTHER PROPERTIES OF THE AVERAGE ENTROPY . GENERATOR THEOREM ..................................... 99 4 MARKOVIAN PAVEMENTS .................................... 109 COMPATIBILITY OF HISTORIES . MARKOVIAN PAVEMENTS ........... 109 MARKOVIAN PAVEMENTS FOR HYPERBOLIC SYSTEMS .............. 119 CODING OF THE VOLUME MEASURE OF SMOOTH HYPERBOLIC SYSTEMS ........................... 141 5 GIBBS DISTRIBUTIONS ....................................... 155 5.1 GIBBS DISTRIBUTIONS ..................................... 155 5.2 PROPERTIES OF GIBBS DISTRIBUTIONS ......................... 165 5.3 GIBBS DISTRIBUTIONS ON Z+ ............................... 170 5.4 AN APPLICATION: EXPANSIVE MAPS OF [0, 1] .................. 180 GENERAL PROPERTIES OF GIBBS AND SRB DISTRIBUTIONS ...... 189 6.1 VARIATIONAL PROPERTIES OF GIBBS DISTRIBUTIONS .............. 189 6.2 APPLICATIONS TO ANOSOV SYSTEMS . SRB DISTRIBUTION ......... 199 4.1 4.2 4.3 6 X CONTENTS 6.3 6.4 EQUIVALENT POTENTIALS . PERIODIC ORBITS. INVARIANT PROBABILITY DISTRIBUTIONS AND ENTROPY ........................................... 208 GIBBS DISTRIBUTIONS WITH TRANSITIVE VACUUM ............... 216 7 ANALYTICITY. SINGULARITY AND PHASE TRANSITIONS ............ 227 7.1 POLYMERS .............................................. 227 7.2 CLUSTER EXPANSIONS ..................................... 240 7.3 RENORMALIZATION BY DECIMATION IN ONE-DIMENSIONAL SYSTEMS ............................. 257 7.4 ABSENCE OF PHASE TRANSITIONS: MORE CRITERIA ............... 270 7.5 PHASE TRANSITIONS ...................................... 276 8 SPECIAL ERGODIC THEORY PROBLEMS IN NONCHAOTIC DYNAMICS .................................. 291 8.1 THEORY OF QUASI-PERIODIC HAMILTONIAN MOTIONS ............. 291 8.2 GRAPHS AND DIAGRAMS FOR THE LINDSTEDT SERIES .............. 299 8.3 CANCELLATIONS .......................................... 307 8.4 CONVERGENCE AND THE KAM THEOREM ...................... 316 9 SOME SPECIAL TOPICS IN KAM THEORY ..................... 327 FOR INVARIANT TORI ....................................... 327 BOUNDS ON RENORMALIZED SERIES . CONVERGENCE .............. 332 SCALING LAWS FOR THE STANDARD MAP ....................... 341 SPECIAL PROBLEMS IN CHAOTIC DYNAMICS ................... 359 10.1 PERTURBING ARNOLDS CAT MAP ............................ 359 10.2 EXTENDED SYSTEMS . LATTICES OF ARNOLDS CAT MAPS .......... 366 10.3 CHAOS IN TIME: AN SRB DISTRIBUTION ..................... 371 10.4 CHAOS IN SPACE-TIME AND SRB DISTRIBUTIONS .............. 381 10.5 ISOMORPHISMS .......................................... 392 9.1 RESUMMATIONS AND RENORMALIZED SERIES 9.2 9.3 9.4 LIMIT FUNCTION FOR THE STANDARD MAP NEAR RESONANCES ...... 352 10 A NONEQUILIBRIUM THERMODYNAMICS? TWENTY-SEVEN COMMENTS ................................. 397 BIBLIOGRAPHY .................................................. 411 NAME INDEX .................................................. 423 SUBJECT INDEX ................................................ 425 CITATIONS INDEX ............................................... 433
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author	Gallavotti, Giovanni Bonetto, Federico Gentile, Guido
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spellingShingle	Gallavotti, Giovanni Bonetto, Federico Gentile, Guido Aspects of ergodic, qualitative and statistical theory of motion Dynamique différentiable Ergodiciteit gtt Mecânica estatística larpcal Mécanique statistique Sistemas dinâmicos diferenciáveis larpcal Statistische mechanica gtt Teoria ergodica larpcal Théorie ergodique Transformations conservant la mesure Differentiable dynamical systems Ergodic theory Measure-preserving transformations Statistical mechanics Statistische Mechanik (DE-588)4056999-8 gnd Ergodentheorie (DE-588)4015246-7 gnd
subject_GND	(DE-588)4056999-8 (DE-588)4015246-7
title	Aspects of ergodic, qualitative and statistical theory of motion
title_auth	Aspects of ergodic, qualitative and statistical theory of motion
title_exact_search	Aspects of ergodic, qualitative and statistical theory of motion
title_full	Aspects of ergodic, qualitative and statistical theory of motion G. Gallavotti ; F. Bonetto ; G. Gentile
title_fullStr	Aspects of ergodic, qualitative and statistical theory of motion G. Gallavotti ; F. Bonetto ; G. Gentile
title_full_unstemmed	Aspects of ergodic, qualitative and statistical theory of motion G. Gallavotti ; F. Bonetto ; G. Gentile
title_short	Aspects of ergodic, qualitative and statistical theory of motion
title_sort	aspects of ergodic qualitative and statistical theory of motion
topic	Dynamique différentiable Ergodiciteit gtt Mecânica estatística larpcal Mécanique statistique Sistemas dinâmicos diferenciáveis larpcal Statistische mechanica gtt Teoria ergodica larpcal Théorie ergodique Transformations conservant la mesure Differentiable dynamical systems Ergodic theory Measure-preserving transformations Statistical mechanics Statistische Mechanik (DE-588)4056999-8 gnd Ergodentheorie (DE-588)4015246-7 gnd
topic_facet	Dynamique différentiable Ergodiciteit Mecânica estatística Mécanique statistique Sistemas dinâmicos diferenciáveis Statistische mechanica Teoria ergodica Théorie ergodique Transformations conservant la mesure Differentiable dynamical systems Ergodic theory Measure-preserving transformations Statistical mechanics Statistische Mechanik Ergodentheorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010537589&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT gallavottigiovanni aspectsofergodicqualitativeandstatisticaltheoryofmotion AT bonettofederico aspectsofergodicqualitativeandstatisticaltheoryofmotion AT gentileguido aspectsofergodicqualitativeandstatisticaltheoryofmotion

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