Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Secants of Trajectories in Dimension Three Read chapter Read first chapter

2013 | OriginalPaper | Chapter

Piecewise Linear Bidimensional Maps as Models of Return Maps for 3D Diffeomorphisms

Authors : A. Pumariño, J. A. Rodríguez, J. C. Tatjer, E. Vigil

Published in: Progress and Challenges in Dynamical Systems

Publisher: Springer Berlin Heidelberg

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The goal of this paper is to study the dynamics of a simple family of piecewise linear maps in dimension two, that we call Expanding Baker Maps (EBM), which is a simplified model of a quadratic limit return map which appears in the study of certain homoclinic bifurcations of two-parameter families of three-dimensional dissipative diffeomorphisms. In spite of its simplicity the EBM capture some of the more relevant dynamics of the quadratic family, specially that related to the evolution of 2D strange attractors.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter The Focus-Center-Limit Cycle Bifurcation in Discontinuous Planar Piecewise Linear Systems Without Sliding
next chapter Practical Stability Domains Near L 4,5 in the Restricted Three-Body Problem: Some Preliminary Facts
Literature
1.
Gonchenko, S.V., Gonchenko, V.S., Tatjer, J.C.: Bifurcations of three-dimensional diffeomorphisms with non-simple quadratic homoclinic tangencies and generalized Hénon maps. Regul. Chaotic Dyn. 12, 233–266 (2007)MathSciNetCrossRefMATH
2.
3.
Palis, J., Takens, F.: Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations. Cambridge University Press, Cambridge (1993)MATH
4.
Palis, J., Viana M.: High dimension diffeomorphisms displaying infinitely many sinks. Ann. Math. 140, 91–136 (1994)MathSciNetCrossRef
5.
Pumariño, A., Tatjer, J.C.: Dynamics near homoclinic bifurcations of three-dimensional dissipative diffeomorphisms. Nonlinearity 19, 2833–2852 (2006)MathSciNetCrossRefMATH
6.
Pumariño, A., Tatjer, J.C.: Attractors for return maps near homoclinic tangencies of three-dimensional dissipative diffeomorphisms. Discret. Contin. Dyn. Syst. Ser. B 8, 971–1006 (2007)CrossRefMATH
7.
Tatjer, J.C.: Three-dimensional dissipative diffeomorphisms with homoclinic tangencies. Ergod. Theory Dyn. Syst. 21, 249–302 (2001)MathSciNetCrossRefMATH
8.
Tatjer, J.C., Simó, C.: Basins of attraction near homoclinic tangencies. Ergod. Theory Dyn. Syst. 14, 351–390 (1994)CrossRefMATH
9.
10.
Metadata
Title
Piecewise Linear Bidimensional Maps as Models of Return Maps for 3D Diffeomorphisms
Authors
A. Pumariño
J. A. Rodríguez
J. C. Tatjer
E. Vigil
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Book
Progress and Challenges in Dynamical Systems

Print ISBN: 978-3-642-38829-3

Electronic ISBN: 978-3-642-38830-9

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-642-38830-9_22

Premium Partner

    Image Credits