Sinha, D.K. Basics of nonlinearities in mathematical sciences

L.: Anthem Press, 2006. - 323p.An attempt to familiarize the reader with nonlinear systems, in particular qualitative characteristics in a variety of systems amenable to mathematization.Preamble
Motivation
Recapturing linear ordinary differential equations
Linear systems : qualitative behaviour
Stability studies
Study of equilibria : another approach
Non-linear vis a vis linear systems
Stability aspects : Liapunov's direct method
Manifolds : introduction and applications in nonlinearity studies
Periodicity : orbits, limit cycles, Poincare map
Bifurcations : a prelude
Catastrophes : a prelude
Theorizing, further, bifurcations and catastrophes
Dynamical systems
Epilogue