In this survey we look at parabolic partial differential equations from a dynamical systems
point of view. With origins deeply rooted in celestial mechanics, and many modern aspects …

In 438 alphabetically-arranged essays, this work provides a useful overview of the core
mathematical background for nonlinear science, as well as its applications to key problems …

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Invariant Measures and the Set of Exceptions to Littlewood's Conjecture Page 1 Annals of
Mathematics, 164 (2006), 513-560 Invariant measures and the set of exceptions to Littlewood's …

It is very unusual for a mathematical or physical idea to disseminate into the society at large.
An interesting example is chaos theory, popularized by Lorenz's butterfly effect:“does the …

Mixing processes occur in many technological and natural applications, with length and time
scales ranging from the very small to the very large. The diversity of problems can give rise …

A bifurcation analysis of the dynamical behavior of a horizontal Rijke tube model is
performed in this paper. The method of numerical continuation is used to obtain the …

High-dimensional systems that have a low-dimensional dominant behavior allow for model
reduction and simplified analysis. We use differential analysis to formalize this important …

Geodesic flows of Riemannian or Finsler manifolds have been the only known contact
Anosov flows. We show that even in dimension 3 the world of contact Anosov flows is vastly …

Chaotic attractors appear in various physical and biological models; however, rigorous
proofs of their existence and bifurcations are rare. In this paper, we construct a simple …