Nonlinear Dynamical Systems and Carleman Linearization
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.
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analytic annihilation ansatz apply approach approximation arbitrary assume Banach space block Bose boson bracket calculate called Carleman embedding Carleman linearization Chapter coherent commutation complex condition conjugation Consider constant convergence corresponding defined Definition denotes described determined difference dimensional discuss domain easily eigenvalues eigenvectors elements evolution Example exists expansion finite formalism formula function functional derivative given Hence Hilbert space holds holomorphic identity independent infinite initial Inserting integrals introduced Lie algebra Lie series linear operator linear system Lorenz mapping matrix means mentioned method multiplicity nonlinear dynamical systems notation Note observable obtain operator ordinary differential equations partial differential equations particular picture polynomial presented proof quantum mechanics relation representation represented respectively resulting satisfies shows solution Steeb Suppose symmetries Taking into account technique Theorem theory transformation values variables vector field write written ди дх
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