Mathematical formulations of the embedding methods commonly used for the reconstruction
of attractors from data series are discussed. Embedding theorems, based on previous work …

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 …

We provide a detailed analysis of the question: how many measurement settings or
outcomes are needed in order to identify an unknown quantum state which is constrained by …

In Shannon theory, lossless source coding deals with the optimal compression of discrete
sources. Compressed sensing is a lossless coding strategy for analog sources by means of …

The purpose of this review is to give a broad outline of the dynamical systems approach to
the two‐dimensional Navier‐Stokes equations. This example has led to much of the theory …

We consider the image of a fractal set X in a Banach space under typical linear and
nonlinear projections into N. We prove that when N exceeds twice the box-counting …

This paper is devoted to the problem of finite-dimensional reduction for parabolic partial
differential equations. We give a detailed exposition of the classical theory of inertial …

Many problems in mathematics and science require the use of infinite-dimensional spaces.
Consequently, there is need for an analogue of the finite-dimensional notions of 'Lebesgue …

This self-contained monograph presents a unified exposition of the thermodynamic
formalism and some of its main extensions, with emphasis on the relation to dimension …

In this paper we first extend the Hölder-Mañé Theorem [1] from a finite dimensional space to
the general Hilbert space setting. Namely, if H is a real Hilbert space and X⊆ H has fractal …