Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

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$Dr. Kai Zehmisch SS 2013 Dipl.-Math. Hella Timmermann 3 ...$

$Prof. Dr. W. Wefelmeyer WS 2004/05 Dipl.-Math. K. Tang Übungen ...$

DMV Tagung 2011 - Köln, 19. - 22. September Olga Voytolovska Universität zu Köln Discontinuity induced Boundary Equilibrium Bifurcations in Filippov systems A rich variety of applications in physics and mechanics can be modeled with non-smooth dynamical systems. Nowadays there is no complete theory for bifurcations of non-smooth systems such as for classical smooth systems. These difficulties arise due to the existence of a discontinuity manifold, separating disjoint regions of the state space. The interaction of invariant sets, e.g. limit cycles and equilibria, with the separating manifold may lead to bifurcations that are not possible in smooth systems. Here we study bifurcations of equilibria in autonomous piecewise smooth discontinuous dynamical systems, called Filippov systems. These are boundary equilibria bifurcations (BEB) that occur as a result of the collision of a pseudo- and a standard-equilibrium branch on the discontinuity manifold. The main focus is on analyzing of 3-dimensional Filippov systems. Based on examples we also illustrate a co-dimension 2 BEB with a non-hyperbolic equilibrium and a system where the existence and absence of a sliding area depend solely on parameter values. The work concludes with an outlook of open problems, especially concerning a possible construction of a center manifold for non-smooth Filippov systems. Daniel Weiss University of Tübingen Existence of Invariant Cones for Piecewise Linear Systems Recently the concept of center manifolds of smooth dynamical systems generated by a pair of complex conjugated eigenvalues with vanishing real part has been carried over to piecewise nonlinear systems. In this process so called invariant cones of corresponding piecewise linear systems play an important role, invariant cones consisting of periodic orbits or orbits spiraling in respectively out. In this talk we derive conditions of existence of invariant cones and study their stability introducing the monodromy matrix of an invariant cone. We apply the results to general 3 dimensional piecewise linear systems and discuss a 6 dimensional brake system. 176
Minisymposium 12 Numerische Finanzmathematik DMV Tagung 2011 - Köln, 19. - 22. September Pascal Heider (Köln), Ralf Korn (Kaiserslautern), Rüdiger Seydel (Köln) Pascal Heider Arbitrage-free Approximation of Call Price Surfaces 179 Christian Jonen Valuing High-Dimensional American-Style Derivatives: A Robust Regression Monte Carlo Method Ralf Korn Recent Advances in Option Pricing with Binomial Trees 180 Jan H. Maruhn Exploiting GPUs and Adjoints for Rapid Monte Carlo Calibrations 180 Kees Oosterlee Efficient valuation methods for contracts in finance and insurance 180 Christoph Winter Wavelet Galerkin schemes for option pricing in multidimensional Lévy models 179 180 177
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Ken Ono Emroy University, Atlanta A
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Markus Linckelmann University of Ab
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Frank Kutzschebauch Universität Be
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Ulrich Derenthal Ludwig-Maximilians
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Myriam-Sonja Hantke Universität zu
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Anna Dall’Acqua Otto-von-Guericke
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André Fischer Center of Smart Inte
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Juliette Hell Freie Universität Be
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Felix Schulze Freie Universität Be
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Eleutherius Symeonidis Katholische
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Felix Schlenk Universität Neuchât
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Markus Richter Karlsruher Institut
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Edgar Brunner Universität Götting
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Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

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