The goal of these lectures is an exposition of the geometric approach to singular
perturbation problems. Singularly perturbed equations gain their special structure from the …

Investigating the dynamics of a network of oscillatory systems is a timely and urgent topic.
Phase synchronization has proven paradigmatic to study emergent collective behavior …

Invariant manifolds are important constructs for the quantitative and qualitative
understanding of nonlinear phenomena in dynamical systems. In nonlinear damped …

In this book we will study equations of the following form x= f (x, t; µ),(0.0. 1) and x↦→ g (x;
µ),(0.0. 2) with x∈ U⊂ Rn, t∈ R1, and µ∈ V⊂ Rp where U and V are open sets in Rn and …

The theory of nonautonomous dynamical systems in both of its formulations as processes
and skew product flows is developed systematically in this book. The focus is on dissipative …

This book develops the theory of global attractors for a class of parabolic PDEs that includes
reaction-diffusion equations and the Navier-Stokes equations, two examples that are treated …

This paper concerns heteroclinic connections and resonance transitions in the planar
circular restricted 3-body problem, with applications to the dynamics of comets and asteroids …

Although mathematics ranks last in the Six Arts (rites, music, archery, chariot racing,
calligraphy and mathematics), it is used in the most practical issues and affairs. Maximally, it …

Existence of'breathers', that is, time-periodic, spatially localized solutions, is proved for a
broad range of time-reversible or Hamiltonian networks of weakly coupled oscillators. Some …

In this survey we discuss current directions of research in the dynamics of nonsmooth
systems, with emphasis on bifurcation theory. An introduction to the state-of-the-art (also for …