The concept of the slow invariant manifold is recognized as the central idea underpinning a
transition from micro to macro and model reduction in kinetic theories. We present the …

The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modeling and the …

3. The Theory of Averaging Page 1 3. The Theory of Averaging 3.1. Introduction This chapter
will be concerned with the theory of averaging for equations in the standard form x =fj(t,x)+f2 …

The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

Poincaré's program for the global analysis of a dynamical system starts by considering
simple solutions, such as equilibria and periodic orbits, together with their corresponding …

Using the recently developed variational theory of hyperbolic Lagrangian coherent
structures (LCSs), we introduce a computational approach that renders attracting and …

By bringing together various ideas and methods for extracting the slow manifolds, the
authors show that it is possible to establish a more macroscopic description in …

The bifurcation diagram of a truncation to six degrees of freedom of the equations for quasi-
geostrophic, baroclinic flow is investigated. Period-doubling cascades and Shil'nikov …

In this paper we prove rigorous results on persistence of invariant tori and their whiskers.
The proofs are based on the parameterization method of [X. Cabré, E. Fontich, R. de la …

Many systems in science and engineering can be modeled as coupled or forced nonlinear
oscillators, which may possess quasi-periodic or phase-locked invariant tori. Since there …