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Chaos for linear operators and abstr...

Kostić, Marko.

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Chaos for linear operators and abstract differential equations /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Chaos for linear operators and abstract differential equations // Marko Kostić.
作者:	Kostić, Marko.
出版者:	Hauppauge :Nova Science Publishers, : c2020.,
面頁冊數:	xxxii, 335 p. ;26 cm.
標題:	Differential equations. -
ISBN:	9781536168952

Chaos for linear operators and abstract differential equations /
Kostić, Marko.

Chaos for linear operators and abstract differential equations /Marko Kostić. - Hauppauge :Nova Science Publishers,c2020. - xxxii, 335 p. ;26 cm. - Mathematics research developments. - Mathematics research developments..

Includes bibliographical references (p. [297]-326) and index.

"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."--Provided by publisher.

ISBN: 9781536168952US230.00

LCCN: 2019955868Subjects--Topical Terms:

517952
Differential equations.

LC Class. No.: QA371 / .K848 2020

Chaos for linear operators and abstract differential equations /
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050 # 4 $a QA371 $b .K848 2020
100 1 $a Kostić, Marko. $3 3470097
245 1 0 $a Chaos for linear operators and abstract differential equations / $c Marko Kostić.
260 # $a Hauppauge : $b Nova Science Publishers, $c c2020.
300 $a xxxii, 335 p. ; $c 26 cm.
490 1 $a Mathematics research developments
504 $a Includes bibliographical references (p. [297]-326) and index.
520 # $a "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."--Provided by publisher.
650 # 0 $a Differential equations. $3 517952
650 # 0 $a Differential equations, Linear. $3 708540
650 # 0 $a Linear operators. $3 576799
830 0 $a Mathematics research developments. $3 3470088