Date : January 28 Speaker : Sebastian Wieczorek Department: Vrije Universiteit, Amsterdam Title : Nonlinear dynamics and bifurcations of an optically injected semiconductor laser Abstract : A single-mode semiconductor laser with optical injection is an example of an experimentally accessible driven nonlinear oscillator. It can be regarded as a generic system of great simplicity on the one hand, and of great technological relevance on the other. Furthermore,understanding this laser system is regarded as a first step towards understanding more complicated systems, such as lasers with delayed optical feedback or mutually coupled lasers. We investigate local and global bifurcations of this laser system using continuation techniques from bifurcation theory. We present a unifying view of the dynamics, study new bifurcation structures and explain how chaotic dynamics appears. This approach gives new insight into nonlinear properties of lasers and allows one to uncover new physical phenomena. Our results stimulated laser experiments on a DFB laser resulting in an unprecedented agreement between theory and experiment on the level of a global bifurcation diagram. An example of a new phenomenon is the effect of multipulse excitability: the injected laser can produce a certain fixed number of pulses after being triggered from its steady state by a single small perturbation. We discovered this effect near codimension--two Bel'yakov homoclinic bifurcations of Shil'nikov homoclinic orbits. This is work with Bernd Krauskopf, Daan Lenstra and Tom Simpson.
Dynamics and Geometry Seminar
Department of Mathematics Cornell University
Mondays 14:30-15.30, MT 205.
organized by warwick@math.cornell.edu
Date : February 07 SPECIAL DYNAMICS/ANALYSIS SEMINAR Speaker : Laura DeMarco Department: Harvard University Title : Dynamics of rational maps: Lyapunov exponents, bifurcations and metrics on the sphere Specials : Thursday, 14:45, MT 310D.
Date : February 18 Speaker : Nikola Petrov Department: University of Texas-Austin Title : Regularity of Conjugacies Between Critical Circle Maps: Numerical Results Abstract : We develop numerical implementations of several criteria to asses the regularity of functions, based on finite difference method and harmonic analysis: Littlewood-Paley theory and wavelet analysis. We study the regularity of conjugacies between critical circle maps (differentiable homeomorphisms with a critical point) with golden mean rotation number. We confirm that several of the features that are predicted by the mathematical results are indeed observable by numerical computation. We obtain that several simple upper bounds seem to be sharp in some cases, but not in others. This indicates that there may be conceptually different mechanisms in play.
Date : March 4 Speaker : John Hubbard Department: Cornell University Title : How to find all roots of complex polynomials by Newton's method. Specials : The lecture will be given in room 251.
Date : April 1 Speaker : Sylvain Bonnot Department: Cornell/Marseille University Title : A proof of Jakobson's theorem Abstract : In 1981, Jakobson showed that in the study of real quadratic polynomials, it was possible to observe with positive probability nice parameters leading to the existence of invariant measures, Lyapunov exponents. The proof will follow a recent article by Yoccoz, with an attempt to use some more geometrical tools, namely the "puzzles".
Date : April 8 Speaker : Sylvain Bonnot Department: Cornell/Marseille University Title : A proof of Jakobson's theorem Abstract : In 1981, Jakobson showed that in the study of real quadratic polynomials, it was possible to observe with positive probability nice parameters leading to the existence of invariant measures, Lyapunov exponents. The proof will follow a recent article by Yoccoz, with an attempt to use some more geometrical tools, namely the "puzzles".
[ version 1.0, 26 January 2002 ]