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Symmetries and Semi-invariants in the Analysis of Nonlinear Systems

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Feldname	Details
Vorliegende Sprache	eng
ISBN	978-0-85729-611-5
Name	Menini, Laura
Name	Tornambè, Antonio
Name ANZEIGE DER KETTE	Tornambè, Antonio
T I T E L	Symmetries and Semi-invariants in the Analysis of Nonlinear Systems
Verlagsort	London
Verlag	Springer-Verlag London Limited
Erscheinungsjahr	2011
Erscheinungsjahr	2011
Umfang	Online-Ressource (X, 324p. 2 illus. in color, digital)
Reihe	SpringerLink. Bücher
Notiz / Fußnoten	Includes bibliographical references and index
Weiterer Inhalt	Symmetries and Semi-invariants in the Analysis of Nonlinear Systems; Preface; Contents; Chapter 1: Notation and Background; 1.1 Notation; 1.2 Analytic and Meromorphic Functions; 1.3 Differential and Difference Equations; 1.4 Differential Forms; 1.5 The Cauchy-Kovalevskaya Theorem; 1.6 The Frobenius Theorem; 1.7 Semi-simple, Normal and Nilpotent Square Matrices; Chapter 2: Analysis of Linear Systems; 2.1 The Linear Centralizer and Linear Normalizer of a Square Matrix; 2.2 Darboux Polynomials and First Integrals; Chapter 3: Analysis of Continuous-Time Nonlinear Systems. 3.1 Semi-invariants and Darboux Polynomials of Continuous-Time Nonlinear Systems3.2 Symmetries and Orbital Symmetries of Continuous-Time Nonlinear Systems; 3.3 Continuous-Time Homogeneous Nonlinear Systems; 3.4 Characteristic Solutions of Continuous-Time Homogeneous Nonlinear Systems; 3.5 Reduction of Continuous-Time Nonlinear Systems; 3.6 Continuous-Time Nonlinear Planar Systems; 3.7 Parameterization of Continuous-Time Nonlinear Planar Systems Having a Given Orbital Symmetry; Case 1: orbital symmetry g=[ P(x1)+Q(x2) 0 ]; Case 2: orbital symmetry g=[ P(x1) Q(x1)]. Case 3: orbital symmetry g=[ P(x1) Q(x2)]Case 4: orbital symmetry g=[ Q(x2)P(x1) 0 ]; 3.8 The Inverse Jacobi Last Multiplier; 3.9 Matrix Integrating Factors; 3.10 Lax Pairs for Continuous-Time Nonlinear Systems; 3.11 A ""Computational"" Result for the Darboux Polynomials of Continuous-Time Nonlinear Systems; 3.12 The Poincaré-Dulac Normal Form of Continuous-Time Nonlinear Systems; 3.13 Homogeneity and Resonance of Continuous-Time Nonlinear Systems; 3.14 The Belitskii Normal Form of Continuous-Time Nonlinear Systems; 3.15 Nonlinear Transformations of Linear Systems. 3.16 Invariant Distributions and Dual Semi-Invariants3.17 Decomposition of Continuous-Time Nonlinear Systems; 3.18 Symmetries of Algebraic Equations; 3.19 Symmetries and Dimensional Analysis; 3.20 Symmetries of Scalar Ordinary Differential Equations; Chapter 4: Analysis of Discrete-Time Nonlinear Systems; 4.1 Semi-invariants and Darboux Polynomials of Discrete-Time Nonlinear Systems; 4.2 A ""Computational"" Result for the Darboux Polynomials of Discrete-Time Nonlinear Systems; 4.3 Symmetries of Discrete-Time Nonlinear Systems; 4.4 Symmetries of Scalar Discrete-Time Nonlinear Systems. 4.5 Reduction of Discrete-Time Nonlinear Systems4.6 A Property of Discrete-Time Nonlinear Planar Systems; 4.7 Lax Pairs for Discrete-Time Nonlinear Systems; 4.8 The Poincaré-Dulac Normal Form for Discrete-Time Nonlinear Systems; 4.9 Linearization of Discrete-Time Nonlinear Systems; 4.10 Homogeneity and Resonance of Discrete-Time Nonlinear Systems; 4.11 The Belitskii Normal Form of Discrete-Time Nonlinear Systems; 4.12 Decomposition of Discrete-Time Nonlinear Systems; Chapter 5: Analysis of Hamiltonian Systems; 5.1 Euler-Lagrange Equations; 5.2 Hamiltonian Systems. 5.3 Normal Forms of Hamiltonian Systems
Titelhinweis	Buchausg. u.d.T.ISBN: 978-0-85729-611-5
ISBN	ISBN 978-0-85729-612-2
Klassifikation	TJFM
	TEC004000
	*93-02
	93C10
	93C95
	93D05
	93C15
	93C55
	93C35
	93C57
	003.75
	629.836
	TJ212-225
Kurzbeschreibung	This book details the analysis of continuous- and discrete-time dynamical systems described by differential and difference equations respectively. Differential geometry provides the tools for this, such as first-integrals or orbital symmetries, together with normal forms of vector fields and of maps. A crucial point of the analysis is linearization by state immersion. The theory is developed for general nonlinear systems and specialized for the class of Hamiltonian systems. By using the strong geometric structure of Hamiltonian systems, the results proposed are stated in a different, less comp
SWB-Titel-Idn	345800958
Signatur	Springer E-Book
Bemerkungen	Elektronischer Volltext - Campuslizenz
Elektronische Adresse	$uhttp://dx.doi.org/10.1007/978-0-85729-612-2
Internetseite / Link	Volltext
Siehe auch	Volltext
Siehe auch	Inhaltsverzeichnis
Siehe auch	Einführung/Vorwort
Siehe auch	Inhaltstext

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