Dr. Stefan Liebscher

Projects

• Dynamics of cosmological models: the tumbling universe
  (DFG Collaborative Research Center 647 on Space, time, matter)
• Analysis of spatio-temporal patterns: kinematics and control
  (DFG Collaborative Research Center 555 on Complex nonlinear processes)
• Structured hybrid models (BMBF)
• Viscous profiles for systems of balance laws
  (DFG Priority Research Program ANumE on Analysis and numerics for conservation laws)

Teaching

• Seminar Dynamics of cosmological models (Summer 2008)
• Exercises BMS-Course Dynamical Systems III (Summer 2008)
• Exercises BMS-Course Partial Differetntial Equations I (Winter 2007/2008)
• Exercises BMS-Course Dynamical Systems II (Winter 2007/2008)
• Seminar Modeling of Dynamical Systems (Summer 2007)
• Exercises BMS-Course Dynamical Systems I (Summer 2007)
• Lecture Topics in Dynamical Systems (Fall 2006)
• Lecture Dynamical systems II (Winter 2005/2006)
• Lecture Dynamical systems I (Summer 2005)
• Exercises Nonlinear Dynamical Systems - Theory and Applications II (Spring 2005)
• Exercises Nonlinear Dynamical Systems - Theory and Applications I (Fall 2004)
• Seminar Hamiltonian dynamics (Summer 2004)
• Exercises Dynamical systems I (Summer 2004)
• Exercises Analysis III (Winter 2003/2004)
• Seminar Functional differential equations (Winter 2003/2004)
• Lecture Singular perturbation theory (Summer 2003)
• Exercises Dynamical systems II (Summer 2003)
• Exercises Dynamical systems I (Winter 2002/2003)
• Exercises Dynamical systems II (Summer 2002)
• Exercises Partial differential equations II (Winter 2001/2002)

Preprints and Publications

Stefan Liebscher:

Stabilität von Entkopplungsphänomenen in Systemen gekoppelter symmetrischer Oszillatoren.
Diplomarbeit, Freie Universität Berlin, 1997.
(gziped postscript, 236 kB)     (pdf, 885 kB)

Bernold Fiedler, Stefan Liebscher, and James C. Alexander:

Generic Hopf bifurcation from lines of equilibria without parameters: I. Theory.
Journal of Differential Equations 167 (2000), pp. 16-35.
(gziped postscript, 238 kB)     (postscript, 2.0 MB)     (pdf, 2.6 MB)

Bernold Fiedler and Stefan Liebscher:

Generic Hopf bifurcation from lines of equilibria without parameters: II. Systems of viscous hyperbolic balance laws.
SIAM Journal on Mathematical Analysis 31 (2000), pp. 1396-1404.
(gziped postscript, 209 kB)     (postscript, 1.9 MB)     (pdf, 2.5 MB)

Bernold Fiedler, Stefan Liebscher, and James C. Alexander:

Generic Hopf bifurcation from lines of equilibria without parameters: III. Binary Oscillations.
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 10 (2000), pp. 1613-1622.
(gziped postscript, 210 kB)     (postscript, 1.9 MB)     (pdf, 2.5 MB)

Stefan Liebscher:

Stable, Oscillatory Viscous Profiles of Weak, non-Lax Shocks in Systems of Stiff Balance Laws.
Dissertation, Freie Universität Berlin, Fachbereich Mathematik und Informatik, 2000.
(gziped postscript, 670 kB)     (pdf, 5.1 MB)

Bernold Fiedler and Stefan Liebscher:

Takens-Bogdanov bifurcations without parameters, and oscillatory shock profiles.
In H. Broer, B. Krauskopf, and G. Vegter, editors, Global Analysis of Dynamical Systems, Festschrift dedicated to Floris Takens for his 60th birthday. IOP, Bristol, 2001, pp. 211-259.
(gziped postscript, 753 kB)     (pdf, 4.5 MB)

Stefan Liebscher:

Stable, oscillatory viscous profiles of weak shocks in systems of stiff balance laws.
In H. Freistühler and G. Warnecke, editors, Hyperbolic Problems: Theory, Numerics, Applications, Eighth International Conference in Magdeburg, February/March 2000. Birkhäuser, Berlin, 2001, pp. 663-672.
(gziped postscript, 2.3 MB)     (pdf, 3.0 MB)

Bernold Fiedler and Stefan Liebscher

Bifurcations without parameters: Some ODE and PDE examples.
In T.-T. Li et al., editors, International Congress of Mathematicians, ICM 2002, Vol. III: Invited Lectures. Higher Education Press, Beijing, 2002, pp. 305-316.
(gziped postscript, 2.2 MB)     (pdf, 2.9 MB)

Jörg Härterich and Stefan Liebscher

Travelling Waves in Systems of Hyperbolic Balance Laws.
In G. Warnecke, editor, Analysis and Numerical Methods for Conservation Laws. Springer-Verlag, 2005, pp. 281-300.
(gziped postscript, 2.4 MB)     (pdf, 3.1 MB)

Andrei Afendikov, Bernold Fiedler and Stefan Liebscher

Plane Kolmogorov fows and Takens-Bogdanov bifurcation without parameters: The doubly reversible case.
Asymptotic Analysis, 2008, in press.
(pdf, 3.3 MB)

Stefan Liebscher

Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters.
Preprint, 2007.
(pdf, 4.0 MB)