Summer 2021

Dynamical Systems 3 - Paralipomena

Prof. Dr. Bernold Fiedler

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Schedule, Sommersemester 2021

Lecture:

Thursday, 10:15-11:45

ONLINE COURSE!

Check the KVV site of the course for information on how to join the lecture. Please, don't hesitate to contact Alejandro in case you want to join, but don't have a KVV account.

Nachklausur:

The Nachklausur (resit exam) will take place on October 12, 10:00-12:00 in the usual online format, you can find more information here (PDF)

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Topics

"Paralipomenon" is Greek and means "additional chapter", "supplement". Depending on the interests of the audience and the time available, we will risk excursions into some of the following topics: bifurcations in discrete dynamical systems, in PDEs, bifurcations and symmetries, global bifurcations, bifurcation without parameter. These complementary topics are intended for those students who still realize that studies are more than the successive acquisition of credit points in modules which are prefabricated to the gusto of Bolognese administrators. They are particularly suitable for the mathematically ambitious, including - but not limited to - the members of the BMS.

See also the lecture Dynamical Systems 3: Bifurcation Theory.

Prerequisites are Dynamical Systems 1 and/or 2.

Basic questions

Basic questions Bifurcation Theory (PDF)
Basic questions Paralipomena (PDF)

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References

• V.S. Afraimovich and S.-B. Hsu: Lectures on Chaotic Dynamical Systems, AMS (2003).
• K.T. Alligood, T.D. Sauer, J.A. Yorke, Chaos: An Introduction to Dynamical Systems, Springer (1996).
• V.I. Arnol’d: Catastrophe Theory, Springer (1984).
• V.I. Arnol’d Geometrical: Methods in the Theory of Ordinary Differential Equations, Springer (1988).
• V.I. Arnold: Ordinary Differential Equations, Springer (1992).
• H. Broer, F. Takens: Dynamical Systems and Chaos, Springer (2011).
• P. Chossat, R. Lauterbach: Methods in Equivariant Bifurcations and Dynamical Systems, World Scientific (2000).
• S.N. Chow and J.K. Hale: Methods of Bifurcation Theory, Springer (1982).
• G. Dangelmayr, K. Kirchgässner, B. Fiedler and A. Mielke: Dynamics of Nonlinear Waves in Dissipative Systems, Addison Wesley (1996).
• B. Fiedler: Global Bifrucation of Periodic Solutions with Symmetry, Springer (1988).
• B. Fiedler and J. Scheurle: Discretization of Homoclinic Orbits, Rapid Forcing and “Invisible” Chaos, Memoirs of the AMS (1996).
• M. Golubitsky and I. Stewart: The Symmetry Perspective, Springer, Birkhäuser (2002).
• M. Golubitsky, I. Stewart and D.G. Schaeffer: Singularities and Groups in Bifurcation Theory, Volumes 1 and 2, Springer (1985, 1988).
• J. Guckenheimer and P. Holmes: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer (1983).
• M.W. Hirsch, S. Smale and R.L. Devaney: Differential Equations, Dynamical Systems, and an Introduction to Chaos, Elsevier (2004).
• A. Katok and B. Hasselblatt: Introduction to the Modern Theory of Dynamical Systems, Cambridge 1997.
• H. Kielhöfer: Bifurcation Theory, an Introduction with Applications to PDEs, Springer (2004).
• Y. Kuznetsov: Elements of Applied Bifurcation Theory, Springer (1995).
• S. Liebscher: Bifurcation without Parameters, Springer (2014).
• J.E. Marsden and M. McCracken: The Hopf Bifurcation and Its Applications, Springer (1976).
• J. Palis and W. de Melo: Geometric Theory of Dynamical Systems, Springer (1982).
• L.P. Shilnikov, A.L. Shilnikov, D.V. Turaev and L.O. Chua: Methods of Qualitative Theory in Nonlinear Dynamics, World Scientific (2001).
• C. Sparrow: The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors, Springer (1982).
• A. Vanderbauwhede: Center Manifolds, Normal Forms and Elementary Bifurcations, in Dynamics Reported Volume 2, John Wiley & Sons (1989).
• A. Vanderbauwhede: Local bifurcation and symmetry, Pitman (1982).
• J. Wainwright and G.F.R. Ellis: Dynamical Systems in Cosmology, Cambridge University Press (1997).
• Handbook of Dynamical Systems, Volumes 1-3, Elsevier (2002-2010).
• Encyclopaedia of Mathematical Sciences: Dynamical Systems, Volumes 1-5, Springer (1994).
• Scholarpedia: Dynamical Systems, doi:10.4249/scholarpedia.1629

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