## Nonlinear Dynamical Systems and Carleman LinearizationThe Carleman linearization has become a new powerful tool in the study of nonlinear dynamical systems. Nevertheless, there is the general lack of familiarity with the Carleman embedding technique among those working in the field of nonlinear models. This book provides a systematic presentation of the Carleman linearization, its generalizations and applications. It also includes a review of existing alternative methods for linearization of nonlinear dynamical systems. There are probably no books covering such a wide spectrum of linearization algorithms. This book also gives a comprehensive introduction to the Kronecker product of matrices, whereas most books deal with it only superficially. The Kronecker product of matrices plays an important role in mathematics and in applications found in theoretical physics. |

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### Contents

Introduction | 7 |

Carleman Embedding Technique | 73 |

Linearization in a Hilbert space | 103 |

Applications | 113 |

Other Linearization Techniques | 153 |

175 | |

### Other editions - View all

Nonlinear Dynamical Systems and Carleman Linearization Krzysztof Kowalski,W.-H. Steeb Limited preview - 1991 |

### Common terms and phrases

analytic functions ansatz arbitrary associate infinite autonomous system Bargmann representation Bose operators boson bracket calculate called Carleman embedding technique Carleman linearization conjugation corresponding defined degrees of freedom denotes diagonal difference equations differential operator domain dynamical systems eigenvalues eigenvectors evolution equation Example expansion finite number Fock space functional derivative Gateaux derivative given Hamilton operator Hamiltonian Heisenberg hermitian hierarchy equations Hilbert space Hilbert space approach Hilbert space formalism identity infinite dimensional infinite linear system inner product introduced isomorphism Kowalski Kronecker product Lemma Lie algebra linear operator Ljapunov exponents Lorenz model mapping matrix method nonlinear dynamical systems nonlinear partial differential nonlinear system notation number of degrees obtain occupation number representation ordinary differential equations Painleve Painleve property Painleve test partial differential equations polynomial quantum mechanics recursion satisfies secular terms Steeb symmetries system 15 Taking into account Theorem theory transformation values variational equation vector field vector space Vries equation written

### Popular passages

Page 177 - Lyberatos G. Steady state bifurcations and exact multiplicity conditions via Carleman linearization, J. Math. Anal. Appl. 126, 143-160, 1987.