TY  - BOOK
AU  - Kozlov,Valery V.
AU  - Furta,Stanislav D.
ED  - SpringerLink (Online service)
TI  - Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations
T2  - Springer Monographs in Mathematics,
SN  - 9783642338175
AV  - QA372 
U1  - 515.352 23
PY  - 2013///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg, Imprint: Springer
KW  - Mathematics
KW  - Dynamics
KW  - Ergodic theory
KW  - Differential equations
KW  - Physics
KW  - Ordinary Differential Equations
KW  - Dynamical Systems and Ergodic Theory
KW  - Mathematical Methods in Physics
N1  - Preface -- Semi-quasihomogeneous systems of ordinary differential equations -- 2. The critical case of purely imaginary kernels -- 3. Singular problems -- 4. The inverse problem for the Lagrange theorem on the stability of equilibrium and other related problems -- Appendix A. Nonexponential asymptotic solutions of systems of functional-differential equations -- Appendix B. Arithmetic properties of the eigenvalues of the Kovalevsky matrix and conditions for the nonintegrability of semi-quasihomogeneous systems of ordinary dierential equations -- Bibliography
N2  - The book is dedicated to the construction of particular solutions of systems of ordinary differential equations in the form of series that are analogous to those used in Lyapunov’s first method. A prominent place is given to asymptotic solutions that tend to an equilibrium position, especially in the strongly nonlinear case, where the existence of such solutions can’t be inferred on the basis of the first approximation alone. The book is illustrated with a large number of concrete examples of systems in which the presence of a particular solution of a certain class is related to special properties of the system’s dynamic behavior. It is a book for students and specialists who work with dynamical systems in the fields of mechanics, mathematics, and theoretical physics
UR  - http://dx.doi.org/10.1007/978-3-642-33817-5
ER  -