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The method of normal forms [[electronic resource] /] / Ali Hasan Nayfeh
| The method of normal forms [[electronic resource] /] / Ali Hasan Nayfeh |
| Autore | Nayfeh Ali Hasan <1933-> |
| Edizione | [2nd, updated and enl. ed.] |
| Pubbl/distr/stampa | Weinheim, Germany, : Wiley-VCH, c2011 |
| Descrizione fisica | 1 online resource (343 p.) |
| Disciplina |
512.9/44
512.944 |
| Soggetto topico |
Normal forms (Mathematics)
Differential equations - Numerical solutions |
| Soggetto genere / forma | Electronic books. |
| ISBN |
3-527-63577-7
1-283-92749-7 3-527-63578-5 3-527-63580-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
The Method of Normal Forms; Contents; Preface; Introduction; 1 SDOF Autonomous Systems; 1.1 Introduction; 1.2 Duffing Equation; 1.3 Rayleigh Equation; 1.4 Duffing-Rayleigh-van der Pol Equation; 1.5 An Oscillator with Quadratic and Cubic Nonlinearities; 1.5.1 Successive Transformations; 1.5.2 The Method of Multiple Scales; 1.5.3 A Single Transformation; 1.6 A General System with Quadratic and Cubic Nonlinearities; 1.7 The van der Pol Oscillator; 1.7.1 The Method of Normal Forms; 1.7.2 The Method of Multiple Scales; 1.8 Exercises; 2 Systems of First-Order Equations; 2.1 Introduction
2.2 A Two-Dimensional System with Diagonal Linear Part2.3 A Two-Dimensional System with a Nonsemisimple Linear Form; 2.4 An n-Dimensional System with Diagonal Linear Part; 2.5 A Two-Dimensional System with Purely Imaginary Eigenvalues; 2.5.1 The Method of Normal Forms; 2.5.2 The Method of Multiple Scales; 2.6 A Two-Dimensional System with Zero Eigenvalues; 2.7 A Three-Dimensional System with Zeroand Two Purely Imaginary Eigenvalues; 2.8 The Mathieu Equation; 2.9 Exercises; 3 Maps; 3.1 Linear Maps; 3.1.1 Case of Distinct Eigenvalues; 3.1.2 Case of Repeated Eigenvalues; 3.2 Nonlinear Maps 3.3 Center-Manifold Reduction3.4 Local Bifurcations; 3.4.1 Fold or Tangent or Saddle-Node Bifurcation; 3.4.2 Transcritical Bifurcation; 3.4.3 Pitchfork Bifurcation; 3.4.4 Flip or Period-Doubling Bifurcation; 3.4.5 Hopf or Neimark-Sacker Bifurcation; 3.5 Exercises; 4 Bifurcations of Continuous Systems; 4.1 Linear Systems; 4.1.1 Case of Distinct Eigenvalues; 4.1.2 Case of Repeated Eigenvalues; 4.2 Fixed Points of Nonlinear Systems; 4.2.1 Stability of Fixed Points; 4.2.2 Classification of Fixed Points; 4.2.3 Hartman-Grobman and Shoshitaishvili Theorems; 4.3 Center-Manifold Reduction 4.4 Local Bifurcations of Fixed Points4.4.1 Saddle-Node Bifurcation; 4.4.2 Nonbifurcation Point; 4.4.3 Transcritical Bifurcation; 4.4.4 Pitchfork Bifurcation; 4.4.5 Hopf Bifurcations; 4.5 Normal Forms of Static Bifurcations; 4.5.1 The Method of Multiple Scales; 4.5.2 Center-Manifold Reduction; 4.5.3 A Projection Method; 4.6 Normal Form of Hopf Bifurcation; 4.6.1 The Method of Multiple Scales; 4.6.2 Center-Manifold Reduction; 4.6.3 Projection Method; 4.7 Exercises; 5 Forced Oscillations of the Duffing Oscillator; 5.1 Primary Resonance; 5.2 Subharmonic Resonance of Order One-Third 5.3 Superharmonic Resonance of Order Three5.4 An Alternate Approach; 5.4.1 Subharmonic Case; 5.4.2 Superharmonic Case; 5.5 Exercises; 6 Forced Oscillations of SDOF Systems; 6.1 Introduction; 6.2 Primary Resonance; 6.3 Subharmonic Resonance of Order One-Half; 6.4 Superharmonic Resonance of Order Two; 6.5 Subharmonic Resonance of Order One-Third; 7 Parametrically Excited Systems; 7.1 The Mathieu Equation; 7.1.1 Fundamental Parametric Resonance; 7.1.2 Principal Parametric Resonance; 7.2 Multiple-Degree-of-Freedom Systems; 7.2.1 The Case of Near 2+1; 7.2.2 The Case of Near 2-1 7.2.3 The Case of Near 2+1 and 3-2 |
| Record Nr. | UNINA-9910130959903321 |
Nayfeh Ali Hasan <1933->
|
||
| Weinheim, Germany, : Wiley-VCH, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The method of normal forms [[electronic resource] /] / Ali Hasan Nayfeh
| The method of normal forms [[electronic resource] /] / Ali Hasan Nayfeh |
| Autore | Nayfeh Ali Hasan <1933-> |
| Edizione | [2nd, updated and enl. ed.] |
| Pubbl/distr/stampa | Weinheim, Germany, : Wiley-VCH, c2011 |
| Descrizione fisica | 1 online resource (343 p.) |
| Disciplina |
512.9/44
512.944 |
| Soggetto topico |
Normal forms (Mathematics)
Differential equations - Numerical solutions |
| ISBN |
3-527-63577-7
1-283-92749-7 3-527-63578-5 3-527-63580-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
The Method of Normal Forms; Contents; Preface; Introduction; 1 SDOF Autonomous Systems; 1.1 Introduction; 1.2 Duffing Equation; 1.3 Rayleigh Equation; 1.4 Duffing-Rayleigh-van der Pol Equation; 1.5 An Oscillator with Quadratic and Cubic Nonlinearities; 1.5.1 Successive Transformations; 1.5.2 The Method of Multiple Scales; 1.5.3 A Single Transformation; 1.6 A General System with Quadratic and Cubic Nonlinearities; 1.7 The van der Pol Oscillator; 1.7.1 The Method of Normal Forms; 1.7.2 The Method of Multiple Scales; 1.8 Exercises; 2 Systems of First-Order Equations; 2.1 Introduction
2.2 A Two-Dimensional System with Diagonal Linear Part2.3 A Two-Dimensional System with a Nonsemisimple Linear Form; 2.4 An n-Dimensional System with Diagonal Linear Part; 2.5 A Two-Dimensional System with Purely Imaginary Eigenvalues; 2.5.1 The Method of Normal Forms; 2.5.2 The Method of Multiple Scales; 2.6 A Two-Dimensional System with Zero Eigenvalues; 2.7 A Three-Dimensional System with Zeroand Two Purely Imaginary Eigenvalues; 2.8 The Mathieu Equation; 2.9 Exercises; 3 Maps; 3.1 Linear Maps; 3.1.1 Case of Distinct Eigenvalues; 3.1.2 Case of Repeated Eigenvalues; 3.2 Nonlinear Maps 3.3 Center-Manifold Reduction3.4 Local Bifurcations; 3.4.1 Fold or Tangent or Saddle-Node Bifurcation; 3.4.2 Transcritical Bifurcation; 3.4.3 Pitchfork Bifurcation; 3.4.4 Flip or Period-Doubling Bifurcation; 3.4.5 Hopf or Neimark-Sacker Bifurcation; 3.5 Exercises; 4 Bifurcations of Continuous Systems; 4.1 Linear Systems; 4.1.1 Case of Distinct Eigenvalues; 4.1.2 Case of Repeated Eigenvalues; 4.2 Fixed Points of Nonlinear Systems; 4.2.1 Stability of Fixed Points; 4.2.2 Classification of Fixed Points; 4.2.3 Hartman-Grobman and Shoshitaishvili Theorems; 4.3 Center-Manifold Reduction 4.4 Local Bifurcations of Fixed Points4.4.1 Saddle-Node Bifurcation; 4.4.2 Nonbifurcation Point; 4.4.3 Transcritical Bifurcation; 4.4.4 Pitchfork Bifurcation; 4.4.5 Hopf Bifurcations; 4.5 Normal Forms of Static Bifurcations; 4.5.1 The Method of Multiple Scales; 4.5.2 Center-Manifold Reduction; 4.5.3 A Projection Method; 4.6 Normal Form of Hopf Bifurcation; 4.6.1 The Method of Multiple Scales; 4.6.2 Center-Manifold Reduction; 4.6.3 Projection Method; 4.7 Exercises; 5 Forced Oscillations of the Duffing Oscillator; 5.1 Primary Resonance; 5.2 Subharmonic Resonance of Order One-Third 5.3 Superharmonic Resonance of Order Three5.4 An Alternate Approach; 5.4.1 Subharmonic Case; 5.4.2 Superharmonic Case; 5.5 Exercises; 6 Forced Oscillations of SDOF Systems; 6.1 Introduction; 6.2 Primary Resonance; 6.3 Subharmonic Resonance of Order One-Half; 6.4 Superharmonic Resonance of Order Two; 6.5 Subharmonic Resonance of Order One-Third; 7 Parametrically Excited Systems; 7.1 The Mathieu Equation; 7.1.1 Fundamental Parametric Resonance; 7.1.2 Principal Parametric Resonance; 7.2 Multiple-Degree-of-Freedom Systems; 7.2.1 The Case of Near 2+1; 7.2.2 The Case of Near 2-1 7.2.3 The Case of Near 2+1 and 3-2 |
| Record Nr. | UNINA-9910829822303321 |
|
Nayfeh Ali Hasan <1933->
|
||
| Weinheim, Germany, : Wiley-VCH, c2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Radially symmetric patterns of reaction-diffusion systems / / Arnd Scheel
| Radially symmetric patterns of reaction-diffusion systems / / Arnd Scheel |
| Autore | Scheel Arnd <1966-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2003] |
| Descrizione fisica | 1 online resource (102 p.) |
| Disciplina |
510 s
515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Reaction-diffusion equations
Bifurcation theory Normal forms (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0384-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Instabilities in one space dimension""; ""1. Introduction""; ""2. Classifying instabilities of reaction-diffusion systems""; ""3. Stationary bifurcations and spatial dynamics""; ""4. Oscillatory bifurcations and spatial dynamics""; ""Chapter 3. Stationary radially symmetric patterns""; ""1. Classification and radial dynamics""; ""2. Center manifolds""; ""3. Expansions and normal forms""; ""4. Matching and transversality""; ""Chapter 4. Time-periodic radially symmetric patterns""; ""1. Radial dynamics on time-periodic functions""
""2. Center manifolds""""3. The reduced vector field for a Hopf instability""; ""4. Heteroclinics in the reduced equation""; ""5. Persistence""; ""Chapter 5. Discussion""; ""1. Stability""; ""2. Beyond radial symmetry""; ""3. Boundaries and holes""; ""4. Concluding remarks""; ""Bibliography"" |
| Record Nr. | UNINA-9910480985203321 |
|
Scheel Arnd <1966->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2003] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Radially symmetric patterns of reaction-diffusion systems / / Arnd Scheel
| Radially symmetric patterns of reaction-diffusion systems / / Arnd Scheel |
| Autore | Scheel Arnd <1966-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2003] |
| Descrizione fisica | 1 online resource (102 p.) |
| Disciplina |
510 s
515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Reaction-diffusion equations
Bifurcation theory Normal forms (Mathematics) |
| ISBN | 1-4704-0384-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Instabilities in one space dimension""; ""1. Introduction""; ""2. Classifying instabilities of reaction-diffusion systems""; ""3. Stationary bifurcations and spatial dynamics""; ""4. Oscillatory bifurcations and spatial dynamics""; ""Chapter 3. Stationary radially symmetric patterns""; ""1. Classification and radial dynamics""; ""2. Center manifolds""; ""3. Expansions and normal forms""; ""4. Matching and transversality""; ""Chapter 4. Time-periodic radially symmetric patterns""; ""1. Radial dynamics on time-periodic functions""
""2. Center manifolds""""3. The reduced vector field for a Hopf instability""; ""4. Heteroclinics in the reduced equation""; ""5. Persistence""; ""Chapter 5. Discussion""; ""1. Stability""; ""2. Beyond radial symmetry""; ""3. Boundaries and holes""; ""4. Concluding remarks""; ""Bibliography"" |
| Record Nr. | UNINA-9910788850103321 |
|
Scheel Arnd <1966->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2003] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Radially symmetric patterns of reaction-diffusion systems / / Arnd Scheel
| Radially symmetric patterns of reaction-diffusion systems / / Arnd Scheel |
| Autore | Scheel Arnd <1966-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2003] |
| Descrizione fisica | 1 online resource (102 p.) |
| Disciplina |
510 s
515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Reaction-diffusion equations
Bifurcation theory Normal forms (Mathematics) |
| ISBN | 1-4704-0384-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Instabilities in one space dimension""; ""1. Introduction""; ""2. Classifying instabilities of reaction-diffusion systems""; ""3. Stationary bifurcations and spatial dynamics""; ""4. Oscillatory bifurcations and spatial dynamics""; ""Chapter 3. Stationary radially symmetric patterns""; ""1. Classification and radial dynamics""; ""2. Center manifolds""; ""3. Expansions and normal forms""; ""4. Matching and transversality""; ""Chapter 4. Time-periodic radially symmetric patterns""; ""1. Radial dynamics on time-periodic functions""
""2. Center manifolds""""3. The reduced vector field for a Hopf instability""; ""4. Heteroclinics in the reduced equation""; ""5. Persistence""; ""Chapter 5. Discussion""; ""1. Stability""; ""2. Beyond radial symmetry""; ""3. Boundaries and holes""; ""4. Concluding remarks""; ""Bibliography"" |
| Record Nr. | UNINA-9910812751403321 |
|
Scheel Arnd <1966->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2003] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Symmetry and perturbation theory in nonlinear dynamics / Giampaolo Cicogna, Giuseppe Gaeta
| Symmetry and perturbation theory in nonlinear dynamics / Giampaolo Cicogna, Giuseppe Gaeta |
| Autore | Cicogna, Giampaolo |
| Pubbl/distr/stampa | Berlin : Springer-Verlag, 1999 |
| Descrizione fisica | xi, 208 p. ; 25 cm. |
| Altri autori (Persone) | Gaeta, Giuseppeauthor |
| Collana | Lecture Notes in Physics. New series m : Monographs ; 57 |
| Soggetto topico |
Differentiable dynamical systems
Normal forms (Mathematics) Perturbation (Mathematics) Symmetry (Physics) |
| ISBN | 3540659048 |
| Classificazione |
53.1.32
510.22 510.34 515'.352 QA614.8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001284349707536 |
|
Cicogna, Giampaolo
|
||
| Berlin : Springer-Verlag, 1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
