"Provides a great deal of material that is completely new to the field of flow invariance, offering fresh insights for experienced mathematicians and rigorous training for students new to the specialty. Four useful appendices supply the methods used throughout the book, making it a totally self-referential and self-contained unit. Features many results that are exclusive to the authors."
"By the way of considered problems and the originality of some approaches, this book is an important reference in pure and applied mathematics, more precisely in nonlinear analysis, optimization, optimal control, ordinary differential equations, partial differential equations, and critical point theory."
---Zentralblatt fur Mathematik, 2000
Tangent vectors to closed sets; flow-invariant sets; second order differential equations and flow-invariance; flow-invariant sets with respect to semilinear differential equations; a transversability approach to flow-invariance; optimization and optimal control via tangential cones; critical point theory on flow-invariant sets; elements of nonlinear analysis; the approximate difference scheme and nonlinear semigroups; Banach manifolds and vector fields; generalized gradients.