Nonlinear Dynamical Systems and Carleman LinearizationWorld Scientific, 1991 - 184 páginas The 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. |
Conteúdo
Introduction | 7 |
Carleman Embedding Technique | 73 |
Linearization in a Hilbert space | 103 |
Applications | 113 |
Other Linearization Techniques | 153 |
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Nonlinear Dynamical Systems And Carleman Linearization Krzysztof Kowalski,Willi-hans Steeb Visualização parcial - 1991 |
Termos e frases comuns
annihilation operators ansatz arbitrary Bargmann representation Bose operators boson c₁ Carleman embedding technique Carleman linearization coherent commutation conjugation Consider corresponding defined denotes difference equations differential operator dynamical systems eigenvalues eigenvectors evolution equation Example expansion finite number Fock space functional derivative Gateaux derivative given H₁ H₂ Hamilton operator Hamiltonian Heisenberg hermitian Hilbert space Hilbert space approach Hilbert space description holomorphic infinite linear system inner product integrals introduced Kowalski Kronecker product Lie algebra linear operator Ljapunov exponents Lorenz model mapping matrix method nonlinear dynamical systems nonlinear partial differential nonlinear system notation number of degrees obtain ordinary differential equations Painlevé property Painlevé test partial differential equations polynomial proof quantum mechanics recursion satisfies secular terms Steeb symmetries Theorem transformation u(uo u₁ variables vector field vector space Vries equation w₁ δι δυ ди მა მე მი