Nonlinear Dynamical Systems And Carleman LinearizationKrzysztof Kowalski, Willi-hans Steeb World Scientific, 26 de mar. de 1991 - 192 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
| 5 | |
Chapter 1 Introduction | 7 |
Chapter 2 Mathematical Preliminaries | 11 |
Chapter 3 Carleman Embedding Technique | 73 |
Chapter 4 Linearization in a Hilbert space | 103 |
Chapter 5 Applications | 113 |
Chapter 6 Other Linearization Techniques | 153 |
| 182 | |
Outras edições - Ver todos
Nonlinear Dynamical Systems and Carleman Linearization Krzysztof Kowalski,W.-H. Steeb Visualização parcial - 1991 |
Termos e frases comuns
analytic functions annihilation operators ansatz arbitrary autonomous system Banach space Bargmann representation Bose annihilation Bose operators bracket Carleman embedding technique Carleman linearization coherent conjugation Consider corresponding defined degrees of freedom denotes 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 identity infinite dimensional infinite linear system inner product introduced isomorphism 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 Painleve property Painleve test partial differential equations polynomial quantum mechanics recursion satisfies secular terms Steeb W.-H symmetries Taking into account Theorem theory transformation vector field vector space Vries equation written