Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

Three-Dimensional Flows

Authors: Araújo, Vítor, Pacifico, Maria José

  • Provides a reference to the main results in the theory with complete proofs and precise statements
  • Presents recent results that provide an extension of the theory of uniform hyperbolicity to flows with attractors having singularities accumulated by regular orbits inside the attractor
  • Includes complete proofs of several results which are spread throughout many different papers with a unified notation and approach
see more benefits

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-3-642-11414-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-3-642-11413-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
price for USA
  • ISBN 978-3-642-26380-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

XXX

About the authors

Both authors are active researchers in the field of Dynamical Systems and Ergodic Theory. One is very young and the other well established in the field, being a coauthor of the main results in the theory.

Reviews

From the reviews:

“The text is well organized and very well presented and certainly this book will be a major reference in this field. Moreover, it is largely self-contained and also the authors are quite careful to present several simplified proofs … .  the book is enriched with numerous figures that illustrate the highly geometric content of this beautiful topic. In conclusion, this book lies at forefront of knowledge in the field and for this reason researchers and students are encouraged … to extend the results explored here.” (Mário Bessa, Mathematical Reviews, Issue 2011 h)

“The present research monograph considers continuous dynamical systems on three-dimensional compact manifolds. … Moreover, several illustrations (partly in color) are present to enhance understanding of the text. In the main body the authors survey the recent results on robustness for 3-flows including both hyperbolic systems and Lorenz-type systems. … As a consequence, it can be recommended as a valuable source for any reader with an advanced background in hyperbolic dynamics.” (G. Teschl, Internationale Mathematische Nachrichten, Issue 217, August, 2011)

“This book presents in a coherent way the results of a long sequence of papers leading to a deep understanding of the behavior of flows on compact 3-manifolds, in particular for the non-conservative setting. It is clearly presented, with a subjective but pertinent and coherent point of view. … it will be the natural reference for those studying the qualitative behavior of vector fields on compact manifolds.” (Christian Bonatti, Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 111, 2012)

“This book deals with the general theory of flows on three-dimensional compact manifolds. … the book under consideration is interesting and presents many results on the dynamical behavior of three dimensional flows with a lot of graphical illustrations which make it more readable.” (Angela Slavova, Zentralblatt MATH, Vol. 1202, 2011)


Table of contents (10 chapters)

  • Introduction

    Araújo, Vítor (et al.)

    Pages 1-4

  • Preliminary Definitions and Results

    Araújo, Vítor (et al.)

    Pages 5-54

  • Singular Cycles and Robust Singular Attractors

    Araújo, Vítor (et al.)

    Pages 55-97

  • Robustness on the Whole Ambient Space

    Araújo, Vítor (et al.)

    Pages 99-121

  • Robust Transitivity and Singular-Hyperbolicity

    Araújo, Vítor (et al.)

    Pages 123-161

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-3-642-11414-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-3-642-11413-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
price for USA
  • ISBN 978-3-642-26380-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Three-Dimensional Flows
Authors
Series Title
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Series Volume
53
Copyright
2010
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-11414-4
DOI
10.1007/978-3-642-11414-4
Hardcover ISBN
978-3-642-11413-7
Softcover ISBN
978-3-642-26380-4
Series ISSN
0071-1136
Edition Number
1
Number of Pages
XIX, 355
Number of Illustrations and Tables
16 illustrations in colour
Topics