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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Chaos for Linear Operators and Abstract Differential Equations (Hardcover)
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Chaos for Linear Operators and Abstract Differential Equations (Hardcover)
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The theory of linear topological dynamics is a rapidly growing
field of research over the last three decades or so. This book
presents a survey of recent results of the author obtained in this
field during the period 2016-2019. Without any doubt, this is the
first research monograph concerning the topological dynamics of
multivalued operators and binary relations, especially, multivalued
linear woperators, simple graphs, digraphs and tournaments (we feel
duty bound to say that multivalued topological dynamics is still a
very undeveloped field of investigation, full of open problems and
possible for further expansion). Asiede from that, the main purpose
of this monograph is to consider topologically dynamical properties
of linear single-valued operators in Frechet spaces and abstract
fractional differential equations in Frechet spaces, which could be
degenerate or non-degenerate in time variable. In this monograph,
we use only two types of fractional derivatives, namely the Caputo
time-fractional derivatives and Weyl time-fractional derivatives.
However, most results on dynamics of differential equations are
given to the abstract differential equations with integer order
derivatives, especially those of first and second order in time.
The monograph is consistsed of two chapters; the first chapter is
further broken down into nine sections, while the second chapter is
broken down into seven sections. It is not of introductory
character to linear topological dynamics and it is not written in a
traditional manner. As in all my previously published monographs,
the numbering of definitions, theorems, propositions, remarks,
lemmas, corollaries, definitions, etc., are by chapter and section;
the bibliography is by author in alphabetic order. Concerning
target audience, wWe deeply believe that the book could be of
invaluable help to experts in linear topological dynamics,
researchers in abstract partial differential equations but and also
to PhD students and advanced graduate students in mathematics as
well. A potential reader should be familiar with backgrounds
including elementary functional analysis, measure and integration
theory as well as the basic theory of abstract (degenerate)
Volterra integro-differential equations. At some places, the
knowledge of graph theory is preferable but not demandedable. This
monograph is not intended to be a comprehensive review of current
trends; albeit includes several recent results from the field of
linear topological dynamics and has more than 450 titles, our
reference list is far from being exhaustively complete.
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