Embedology
Mathematical formulations of the embedding methods commonly used for the reconstruction
of attractors from data series are discussed. Embedding theorems, based on previous work …
of attractors from data series are discussed. Embedding theorems, based on previous work …
[图书][B] Infinite-dimensional dynamical systems: an introduction to dissipative parabolic PDEs and the theory of global attractors
JC Robinson - 2001 - books.google.com
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 …
reaction-diffusion equations and the Navier-Stokes equations, two examples that are treated …
Quantum tomography under prior information
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 …
outcomes are needed in order to identify an unknown quantum state which is constrained by …
Rényi information dimension: Fundamental limits of almost lossless analog compression
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 …
sources. Compressed sensing is a lossless coding strategy for analog sources by means of …
Attractors and Finite‐Dimensional Behaviour in the 2D Navier‐Stokes Equations
JC Robinson - International Scholarly Research Notices, 2013 - Wiley Online Library
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 …
the two‐dimensional Navier‐Stokes equations. This example has led to much of the theory …
Regularity of embeddings of infinite-dimensional fractal sets into finite-dimensional spaces
BR Hunt, VY Kaloshin - Nonlinearity, 1999 - iopscience.iop.org
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 …
nonlinear projections into N. We prove that when N exceeds twice the box-counting …
Inertial manifolds and finite-dimensional reduction for dissipative PDEs
S Zelik - Proceedings of the Royal Society of Edinburgh Section …, 2014 - cambridge.org
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 …
differential equations. We give a detailed exposition of the classical theory of inertial …
Prevalence
W Ott, J Yorke - Bulletin of the American Mathematical Society, 2005 - ams.org
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 …
Consequently, there is need for an analogue of the finite-dimensional notions of 'Lebesgue …
[图书][B] Thermodynamic formalism and applications to dimension theory
L Barreira - 2011 - books.google.com
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 …
formalism and some of its main extensions, with emphasis on the relation to dimension …
Finite fractal dimension and Hölder-Lipschitz parametrization
C Foias, E Olson - Indiana University Mathematics Journal, 1996 - JSTOR
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 …
the general Hilbert space setting. Namely, if H is a real Hilbert space and X⊆ H has fractal …