## Nonlinear Dynamical Systems and Carleman LinearizationFor mathematicians and physicists at an advanced graduate or professional level, explains a new method for studying nonlinear dynamical systems called the Carleman linearization, or Carleman embedding technique. Also surveys other techniques. Acidic paper. Annotation copyrighted by Book News, Inc., Portland, OR |

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### Contents

Introduction | 7 |

Carleman Embedding Technique | 73 |

Linearization in a Hilbert space | 103 |

Applications | 113 |

Other Linearization Techniques | 153 |

175 | |

### 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.