PD Dr. Stefan Liebscher

Projects

• Mathematical Physics: Dynamics and Nonlinear Evolution Equations in General Relativity
  (DFG Collaborative Research Center 647 on Space, time, matter)
• Dynamics of cosmological models: the tumbling universe
  (DFG Collaborative Research Center 647 on Space, time, matter)
• Singularity structure, longtime behaviour and dynamics of solutions of nonlinear evolution equations
  (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

• Lecture Projective Geometry (Summer 2015)
• Lecture Analysis III (Winter 2014/2015)
• Exercises Analysis I (Winter 2012)
• Seminar Blow Up in Dynamical Systems (Summer 2012)
• Exercises Infinite-dimensional Dynamical Systems / Sturm Attractors (Summer 2012)
• Seminar Infinite-simensional Dynamical System / Semigroups (Winter 2011/12)
• Seminar Bifurcation theory (Summer 2011)
• Exercises BMS-Course Dynamical Systems III (Summer 2011)
• Seminar Delay Equations (Winter 2010/2011)
• Exercises BMS-Course Dynamical Systems II (Winter 2010/2011)
• Seminar Dynamics' (Hi)stories (Summer 2010)
• Exercises BMS-Course Dynamical Systems I (Summer 2010)
• Exercises Analysis III (Winter 2009/2010)
• Seminar Analysis' (Hi)stories (Summer 2009)
• Exercises Analysis II (Summer 2009)
• Seminar Infinite Dimensional Dynamical Systems (Winter 2008/2009)
• Exercises Analysis I (Winter 2008/2009)
• 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, 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, 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, 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, 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, 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.
(arxiv.org/abs/math/0304453)

Jörg Härterich, 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, Stefan Liebscher, Bernold Fiedler

Standing waves near the Kolmogorov flow.
Doklady Mathematics 75 (2007), pp. 283-286,
translation from Doklady Akademii Naukk 413 (2007), 587-590.

Andrei Afendikov, Bernold Fiedler, Stefan Liebscher

Plane Kolmogorov flows and Takens-Bogdanov bifurcation without parameters: The doubly reversible case.
Asymptotic Analysis 60 (2008), pp. 135-211.
(pdf, 3.3 MB) (journal)

Andrei Afendikov, Bernold Fiedler, Stefan Liebscher

Plane Kolmogorov flows and Takens-Bogdanov bifurcation without parameters. The singly reversible case.
Asymptotic Analysis 72 (2011), pp. 31-76.
(journal)

Stefan Liebscher

Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters.
Electronic Journal of Differential Equations 2011 (2011), No. 63, pp. 1-12.
(arxiv.org/abs/1004.3410)

Stefan Liebscher, Jörg Härterich, Kevin Webster, Marc Georgi

Ancient dynamics in Bianchi models: Approach to Periodic Cycles.
Communications in Mathematial Physics 305 (2011), pp. 59-83.
(arxiv.org/abs/1004.1989)

Stefan Liebscher, Alan D. Rendall, Sophonie Blaise Tchapnda

Oscillatory singularities in Bianchi models with magnetic fields.
Annales Henry Poincaré 14 (2013), No. 5, pp. 1043--1075.
(arxiv.org/abs/1207.2655)

Stefan Liebscher

Bifurcation without parameters.
Habilitationsschrift, Freie Universitiät Berlin, 2012.
(pdf, 15 MB)

Stefan Liebscher

Bifurcation without parameters.
Lecture Notes in Mathematics 2117, Springer-Verlag, 2015, 142 pages.
(publisher)

Anna Karnauhova, Stefan Liebscher

Connected components of meanders: I. Bi-rainbow meanders.
submitted 2015.
(arxiv.org/abs/1504.03099)