Skip to main content
  • Book
  • © 2014

Dynamical Systems Generated by Linear Maps

  • Provides explicit answers to specific questions being useful in applications

  • Investigates dynamical system given by linear mapping

  • Offers a natural amplification, refinement and supplement to linear algebra and dynamical systems theory textbooks

  • Includes supplementary material: sn.pub/extras

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

This is a preview of subscription content, log in via an institution to check for access.

Table of contents (15 chapters)

  1. Front Matter

    Pages i-xii
  2. Introduction

    • Ćemal B. Dolićanin, Anatolij B. Antonevich
    Pages 1-6
  3. Vector Trajectory

    1. Front Matter

      Pages 7-7
    2. The Jordan Basis and Special Subspaces

      • Ćemal B. Dolićanin, Anatolij B. Antonevich
      Pages 9-15
    3. Representation of the Vector Trajectory

      • Ćemal B. Dolićanin, Anatolij B. Antonevich
      Pages 17-28
    4. The Structures Related to the Principal Term of the Vector Trajectory

      • Ćemal B. Dolićanin, Anatolij B. Antonevich
      Pages 29-44
  4. Subspace Trajectory

    1. Front Matter

      Pages 61-61
    2. Subspaces

      • Ćemal B. Dolićanin, Anatolij B. Antonevich
      Pages 63-79
    3. The Action of a Linear Map on the Grassmann Manifold

      • Ćemal B. Dolićanin, Anatolij B. Antonevich
      Pages 81-88
    4. The Exterior Algebra and Subspaces

      • Ćemal B. Dolićanin, Anatolij B. Antonevich
      Pages 89-97
    5. The Algebraic Approach to the Study of Subspace Trajectory

      • Ćemal B. Dolićanin, Anatolij B. Antonevich
      Pages 99-106
    6. The Geometric Approach

      • Ćemal B. Dolićanin, Anatolij B. Antonevich
      Pages 107-112
    7. The Geometric Approach: An Operator with One Point Spectrum

      • Ćemal B. Dolićanin, Anatolij B. Antonevich
      Pages 113-139
    8. The Convergence of a Subspace Trajectory for an Arbitrary Operator

      • Ćemal B. Dolićanin, Anatolij B. Antonevich
      Pages 141-155
  5. The Applications to Weighted Shift Operators

    1. Front Matter

      Pages 157-157
    2. The Spectrum of Weighted Shift Operator

      • Ćemal B. Dolićanin, Anatolij B. Antonevich
      Pages 159-176
    3. The Subtle Spectral Properties

      • Ćemal B. Dolićanin, Anatolij B. Antonevich
      Pages 177-184
    4. The Weighted Shift Operators in Spaces of Vector Functions

      • Ćemal B. Dolićanin, Anatolij B. Antonevich
      Pages 185-199
  6. Back Matter

    Pages 201-203

About this book

The book deals with dynamical systems, generated by linear mappings of finite dimensional spaces and their applications. These systems have a relatively simple structure from the point of view of the modern dynamical systems theory. However, for the dynamical systems of this sort, it is possible to obtain explicit answers to specific questions being useful in applications.

The considered problems are natural and look rather simple, but in reality in the course of investigation, they confront users with plenty of subtle questions and their detailed analysis needs a substantial effort.

The problems arising are related to linear algebra and dynamical systems theory, and therefore, the book can be considered as a natural amplification, refinement and supplement to linear algebra and dynamical systems theory textbooks.

Reviews

From the book reviews:

“This is an excellent book that can be used for a third or fourth year graduate course in dynamical systems or a related field. … there is a good solid bibliography and pertinent references (both books and journal articles) making the book ideal for a seminar type presentation where students participate in the course with presentation of papers.” (Russell Jay Hendel, MAA Reviews, January, 2015)

Authors and Affiliations

  • State University of Novi Pazar, Novi Pazar, Serbia

    Ćemal B. Dolićanin

  • Belarusian State University, Minsk, Belarus

    Anatolij B. Antonevich

About the authors

Ćemal B. Dolićanin (Cemal B. Dolicanin), full Professor of Mathematics at the State University of Novi Pazar, Republic of Serbia. He is a member of South Slavic Academy of Non-linear Sciences (JANN). He published 90 scientific papers in Theoretical Mathematics, Geometry, Dynamical Systems Theory and Applied Mathematics in Engineering Sciences. Applications from these papers are published in 26 textbooks and monographs.
e-mail: cdolicanin@np.ac.rs

Anatolij B. Antonevich, full Professor of Mathematics at Belarusian State University, Minsk, Belarus and he is a Professor of Mathematics at the University of Bialystok, Poland. He is the author of 250 scientific papers in Functional Analysis and its applications are published in 15 monographs and textbooks.
e-mail: antonevich@bsu.by

Bibliographic Information

  • Book Title: Dynamical Systems Generated by Linear Maps

  • Authors: Ćemal B. Dolićanin, Anatolij B. Antonevich

  • DOI: https://doi.org/10.1007/978-3-319-08228-8

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2014

  • Hardcover ISBN: 978-3-319-08227-1Published: 01 August 2014

  • Softcover ISBN: 978-3-319-35830-7Published: 10 September 2016

  • eBook ISBN: 978-3-319-08228-8Published: 19 July 2014

  • Edition Number: 2

  • Number of Pages: XII, 203

  • Additional Information: Originally published by Academska Misao, Belgrade, 2012

  • Topics: Dynamical Systems and Ergodic Theory, Vibration, Dynamical Systems, Control, Complexity

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access