[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index

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Differential Equations and Dynamical Systems

Real and Complex Analysis

General Topology-I

In this paper we determine the distributional behavior of sums of free (in the sense of Voiculescu) identically distributed, inflnitesimal random variables. The theory is shown to parallel the classical theory of independent random variables, though the limit laws are usually quite difierent. Our work subsumes all previously known instances of weak convergence of sums of free, identically distributed random variables. In particular, we determine the domains of attraction of stable distributions in the free theory. These freely stable distributions are studied in detail in the appendix, where their unimodality and duality properties are demonstrated.

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Stable laws and domains of attraction in free probability theory

Attractors for a damped hyperbolic equation with linear memory

This paper is concerned with the semilinear strongly damped wave equation The existence of compact global attractors of optimal regularity is proved for nonlinearities of critical and supercritical growth.

https://iopscience.iop.org/article/10.1088/0951-7715/19/7/001/pdf

Smooth attractors for strongly damped wave equations

http://www.im.ufrj.br/~rivera/Art_Pub/Italia02.pdf

Global Attractors for a Semilinear Hyperbolic Equation in Viscoelasticity

The study of nonlinear dynamical systems is of basic importance in the understanding of several natural phenomena. If a certain mathematical model is described by a nonlinear dynamical system, then it is usually difficult to predict whether or not the system will evolve towards a stationary state or it will exhibit a chaotic behavior. The sensibility to the initial conditions and to the parameters characterizing the nonlinear system show that a correct approach to study its dynamics should be more geometric. This means that the evolution system must be treated as an ordinary differential equation whose solutions (trajectories) can be viewed as curves in a suitable phase space, possibly of infinite dimension. We recall, for instance, that the chaotic behavior of some nonlinear system can be explained by the existence of a so-called strange attractor, that is, a set, usually of finite fractal dimension, which attracts uniformly any trajectory. Actually, this means that in the long run the dynamics of an infinite-dimensional system is controlled by a finite number of parameters and this can be of some help for possible numerical approximations.

Vittorino Pata

Papers

Stable laws and domains of attraction in free probability theory

Attractors for a damped hyperbolic equation with linear memory

Smooth attractors for strongly damped wave equations

Global Attractors for a Semilinear Hyperbolic Equation in Viscoelasticity

Uniform attractors of nonautonomous dynamical systems with memory