Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations

✍ Scribed by V V Kozlov; Stanislav D Furta; Lester Senechal

• Publisher: Springer
• Year: 2013
• Tongue: English
• Leaves: 278
• Series: Springer monographs in mathematics
• Category: Library

✦ Synopsis

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 proper Read more...

✦ Table of Contents

Cover......Page 1
Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations......Page 4
Translator’s Note......Page 6
Preface......Page 8
Contents......Page 10
Introduction......Page 12
1.1 Formal Asymptotic Particular Solutions of Semi-quasihomogeneous Systems of Differential Equations......Page 21
1.2 Problems of Convergence......Page 33
1.3 Exponential Methods for Finding Nonexponential Solutions......Page 44
1.4 Examples......Page 61
1.5 Group Theoretical Interpretation......Page 75
2.1 Asymptotic Solutions of Autonomous Systems of Differential Equations in the Critical Case of m Pairs of Pure Imaginary and n-2m Zero Roots of the Characteristic Equation......Page 96
2.2 Periodic and Quasiperiodic Systems......Page 111
2.3 Hamiltonian Systems......Page 127
3.1 Asymptotic Solutions of Autonomous Systems of Differential Equations in the Critical Case of Zero Roots of the Characteristic Equation......Page 150
3.2 Concerning Iterated Logarithms......Page 162
3.3 Systems Implicit with Respect to Higher Derivatives and Kuznetsov's Theory......Page 171
4.1 On Energy Criteria for Stability......Page 187
4.2 Regular Problems......Page 207
4.3 Singular Problems......Page 218
Appendix
A Nonexponential Asymptotic Solutions of Systems of Functional-Differential Equations......Page 233
Appendix
B Arithmetic Properties of the Eigenvalues of the Kovalevsky Matrix and Conditions for the Nonintegrability of Semi-quasihomogeneous Systems of Ordinary Differential Equations......Page 246
Literature......Page 266
Index......Page 275