4-6 May 2010 –– MRI Master Class Mini-Course Computing Invariant Manifolds via the Continuation of Orbit Segments

Hinke Osinga (H.M.Osinga@bristol.ac.uk )			This mini-course focusses on the idea of representing a two-dimensional invariant global manifold of a dynamical system as a family of orbit segments, which can then be computed as a solution family of a suitable BVP using AUTO. Literature: Computing invariant manifolds via the continuation of orbit segments B. Krauskopf and H. M. Osinga in B. Krauskopf, H. M. Osinga and J. Galán-Vioque (Eds.), Numerical Continuation Methods for Dynamical Systems: Path following and boundary value problems, Springer-Verlag (2007), pp. 117–154. (Local copy.) A survey of methods for computing (un)stable manifolds of vector fields B. Krauskopf, H. M. Osinga, E. J. Doedel, M. E. Henderson, J. M. Guckenheimer, A. Vladimirsky, M. Dellnitz and O. Junge International Journal of Bifurcation & Chaos 15(3): 763–791, 2005. (Local copy.) Global bifurcations of the Lorenz manifold E. J. Doedel, B. Krauskopf and H. M. Osinga Nonlinearity 19(12): 2947–2972, 2006; with multimedia supplement. (Local copy.) Investigating the consequences of global bifurcations for two-dimensional invariant manifolds of vector fields bifurcations of the Lorenz manifold P. Aguirre, JE. J. Doedel, B. Krauskopf and H. M. Osinga Discrete and Continuous Dynamical Systems — Series S (in press). (Local copy.)
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