Differentiable dynamics : an introduction to the orbit structure of diffeomorphisms
著者
書誌事項
Differentiable dynamics : an introduction to the orbit structure of diffeomorphisms
M.I.T. Press, c1971
- : pbk
大学図書館所蔵 全68件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Bibliography: p. 267-278
Includes index
内容説明・目次
内容説明
The subject of differentiable dynamical systems in the form recently developed by the group of mathematicians associated with S. Smale and M. Peixoto in the United States and with Ja. Sinai and D. Asonov in the Soviet Union is evoking great interest among this generation's mathematicians. Specialists teaching courses in this field as well as nonexperts interested in a comprehensive introduction should welcome "Differentiable Dynamics, " the first work to collect and explain in detail a wide selection of results and techniques which have formerly been scattered in the primary literature.Approaching this literature directly can, moreover, be somewhat treacherous since a number of obsolete results are embedded within it. In this regard, it is worth noting that one expert in this area who examined the book in manuscript wrote, "Nitecki has it seems to me made an admirable choice of material--both in what he has put in and what he has left out." Some of this material is so recent that at present it exists only in preprint form.The book has already proved itself from the standpoint of text use; it derives from a set of lecture notes prepared by the author for a graduate course in dynamical systems he conducted at Yale. Beyond the seminar room, mathematicians generally working in the area of topology and global analysis should find it a useful reference for the recent work in dynamics on manifolds.The book begins with an introduction to the Smale program and philosophy and goes on to give a detailed account of the subject, developing it from the simple case of the circle since all the topological complications of higher dimensions are absent but all the essential features of the subject are clearly visible. With this preparation, the student is able to proceed to the inherently difficult "horseshoe example" and its relation to symbolic dynamics."Differentiable Dynamics" consists of the following chapters: Introduction: Flows and Diffeomorphisms--Preliminaries--The Circle--Periodic Points--Anosov Diffeomorphisms--The Horseshoe--Hyperbolic Sets--The -Stability Theorem--A Survey of Recent Work.
「Nielsen BookData」 より