國立虎尾科技大學 |

Perturbation Theory = Mathematics, Methods and Applications /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Perturbation Theory/ edited by Giuseppe Gaeta.
其他題名:	Mathematics, Methods and Applications /
其他作者:	Gaeta, Giuseppe.
面頁冊數:	99 illus., 20 illus. in color. eReference.online resource. :
Contained By:	Springer Nature eReference
標題:	Evolutionary Biology. -
電子資源:	https://doi.org/10.1007/978-1-0716-2621-4
ISBN:	9781071626214

Perturbation Theory = Mathematics, Methods and Applications /
Perturbation TheoryMathematics, Methods and Applications /[electronic resource] :edited by Giuseppe Gaeta. - 1st ed. 2022. - 99 illus., 20 illus. in color. eReference.online resource. - Encyclopedia of Complexity and Systems Science Series,2629-2343. - Encyclopedia of Complexity and Systems Science Series,.

Diagrammatic Methods in Classical Perturbation Theory -- Hamiltonian Perturbation Theory (and Transition to Chaos) -- Kolmogorov-Arnold-Moser (KAM) Theory for Finite and Infinite Dimensional Systems -- n-Body Problem and Choreographies -- Nekhoroshev Theory -- Symmetry and Perturbation Theory in Non-linear Dynamics -- Normal Forms in Perturbation Theory -- Perturbation Analysis of Parametric Resonance -- Perturbation of Equilibria in the Mathematical Theory of Evolution -- Perturbation of Systems with Nilpotent Real Part -- Perturbation Theory -- Perturbation Theory in Celestial Mechanics -- Introduction to Perturbation Theory -- Perturbation Theory and Molecular Dynamics -- Perturbation Theory for Non-smooth Systems -- Perturbation Theory for PDEs -- Perturbation Theory in Quantum Mechanics -- Semiclassical Perturbation Theory -- Convergence of Perturbative Expansions -- Quantum Bifurcations -- Perturbation of superintegrable systems -- Computational methods in perturbation theory -- Perturbation theory in general relativity and cosmology -- Perturbation Theory for Water Waves -- Perturbation Theory and the Method of Detuning.

This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, is devoted to the fundamentals of Perturbation Theory (PT) as well as key applications areas such as Classical and Quantum Mechanics, Celestial Mechanics, and Molecular Dynamics. Less traditional fields of application, such as Biological Evolution, are also discussed. Leading scientists in each area of the field provide a comprehensive picture of the landscape and the state of the art, with the specific goal of combining mathematical rigor, explicit computational methods, and relevance to concrete applications. New to this edition are chapters on Water Waves, Rogue Waves, Multiple Scales methods, legged locomotion, Condensed Matter among others, while all other contributions have been revised and updated. Coverage includes the theory of (Poincare’-Birkhoff) Normal Forms, aspects of PT in specific mathematical settings (Hamiltonian, KAM theory, Nekhoroshev theory, and symmetric systems), technical problems arising in PT with solutions, convergence of series expansions, diagrammatic methods, parametric resonance, systems with nilpotent real part, PT for non-smooth systems, and on PT for PDEs [write out this acronym partial differential equations]. Another group of papers is focused specifically on applications to Celestial Mechanics, Quantum Mechanics and the related semiclassical PT, Quantum Bifurcations, Molecular Dynamics, the so-called choreographies in the N-body problem, as well as Evolutionary Theory. Overall, this unique volume serves to demonstrate the wide utility of PT, while creating a foundation for innovations from a new generation of graduate students and professionals in Physics, Mathematics, Mechanics, Engineering and the Biological Sciences.

ISBN: 9781071626214

Standard No.: 10.1007/978-1-0716-2621-4doiSubjects--Topical Terms:

668573
Evolutionary Biology.

LC Class. No.: QC19.2-20.85

Dewey Class. No.: 530.1

Perturbation Theory = Mathematics, Methods and Applications /
LDR:04281nam a22003855i 4500 001 1086455
003 DE-He213
005 20221216091924.0
007 cr nn 008mamaa
008 221228s2022 xxu| s |||| 0|eng d
020 $a 9781071626214 $9 978-1-0716-2621-4
024 7 $a 10.1007/978-1-0716-2621-4 $2 doi
035 $a 978-1-0716-2621-4
050 4 $a QC19.2-20.85
072 7 $a PHU $2 bicssc
072 7 $a SCI040000 $2 bisacsh
072 7 $a PHU $2 thema
082 0 4 $a 530.1 $2 23
245 1 0 $a Perturbation Theory $h [electronic resource] : $b Mathematics, Methods and Applications / $c edited by Giuseppe Gaeta.
250 $a 1st ed. 2022.
264 1 $a New York, NY : $b Springer US : $b Imprint: Springer, $c 2022.
300 $a 99 illus., 20 illus. in color. eReference. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Encyclopedia of Complexity and Systems Science Series, $x 2629-2343
505 0 $a Diagrammatic Methods in Classical Perturbation Theory -- Hamiltonian Perturbation Theory (and Transition to Chaos) -- Kolmogorov-Arnold-Moser (KAM) Theory for Finite and Infinite Dimensional Systems -- n-Body Problem and Choreographies -- Nekhoroshev Theory -- Symmetry and Perturbation Theory in Non-linear Dynamics -- Normal Forms in Perturbation Theory -- Perturbation Analysis of Parametric Resonance -- Perturbation of Equilibria in the Mathematical Theory of Evolution -- Perturbation of Systems with Nilpotent Real Part -- Perturbation Theory -- Perturbation Theory in Celestial Mechanics -- Introduction to Perturbation Theory -- Perturbation Theory and Molecular Dynamics -- Perturbation Theory for Non-smooth Systems -- Perturbation Theory for PDEs -- Perturbation Theory in Quantum Mechanics -- Semiclassical Perturbation Theory -- Convergence of Perturbative Expansions -- Quantum Bifurcations -- Perturbation of superintegrable systems -- Computational methods in perturbation theory -- Perturbation theory in general relativity and cosmology -- Perturbation Theory for Water Waves -- Perturbation Theory and the Method of Detuning.
520 $a This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, is devoted to the fundamentals of Perturbation Theory (PT) as well as key applications areas such as Classical and Quantum Mechanics, Celestial Mechanics, and Molecular Dynamics. Less traditional fields of application, such as Biological Evolution, are also discussed. Leading scientists in each area of the field provide a comprehensive picture of the landscape and the state of the art, with the specific goal of combining mathematical rigor, explicit computational methods, and relevance to concrete applications. New to this edition are chapters on Water Waves, Rogue Waves, Multiple Scales methods, legged locomotion, Condensed Matter among others, while all other contributions have been revised and updated. Coverage includes the theory of (Poincare’-Birkhoff) Normal Forms, aspects of PT in specific mathematical settings (Hamiltonian, KAM theory, Nekhoroshev theory, and symmetric systems), technical problems arising in PT with solutions, convergence of series expansions, diagrammatic methods, parametric resonance, systems with nilpotent real part, PT for non-smooth systems, and on PT for PDEs [write out this acronym partial differential equations]. Another group of papers is focused specifically on applications to Celestial Mechanics, Quantum Mechanics and the related semiclassical PT, Quantum Bifurcations, Molecular Dynamics, the so-called choreographies in the N-body problem, as well as Evolutionary Theory. Overall, this unique volume serves to demonstrate the wide utility of PT, while creating a foundation for innovations from a new generation of graduate students and professionals in Physics, Mathematics, Mechanics, Engineering and the Biological Sciences.
650 2 4 $a Evolutionary Biology. $3 668573
650 2 4 $a Classical Mechanics. $3 1140387
650 2 4 $a Civil Engineering. $3 669250
650 2 4 $a Mathematical Physics. $3 786661
650 1 4 $a Theoretical, Mathematical and Computational Physics. $3 768900
650 0 $a Evolution (Biology). $3 686236
650 0 $a Mechanics. $3 527684
650 0 $a Civil engineering. $3 561339
650 0 $a Mathematical physics. $3 527831
700 1 $a Gaeta, Giuseppe. $4 edt $4 http://id.loc.gov/vocabulary/relators/edt $3 1199251
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eReference
776 0 8 $i Printed edition: $z 9781071626207
830 0 $a Encyclopedia of Complexity and Systems Science Series, $x 2629-2343 $3 1365784
856 4 0 $u https://doi.org/10.1007/978-1-0716-2621-4
912 $a ZDB-2-PHA
912 $a ZDB-2-SXRP
950 $a Physics and Astronomy (SpringerNature-11651)
950 $a Reference Module Physical and Materials Science (SpringerNature-43751)