For more information about this meeting, contact Dmitri Burago.
|Title:||Grazing bifurcation and non-hyperbolic equilibria of strongly nonlinear dynamical systems|
|Seminar:||Center for Dynamics and Geometry Seminars|
|Speaker:||S. G. Kryzhevich, Saint-Petersburg State University, Russia|
|We consider the grazing bifurcation, which is typical for dynamical systems with discontinuous right hand sides and is one of common reason for chaotic behavior in such kind of systems. This bifurcation corresponds to the case when a periodic solution is tangent to the boundary of one of domains where the vector field of the system is continuous.
The properties of periodic solutions of strongly nonlinear systems, like vibro-impact systems or ones with a dry friction may change very quickly as one changes the parameters of the system. The ratios of their Lyapunov exponents may be big and even the dimensions of their stable and unstable manifolds may be difficult to be calculated.
However, the theory of non-hyperbolic equilibria (and, more generally, one of the partial hyperbolicity) can be applied for the considered case. We start with a general case of a diffeomorphism of a smooth man- ifold or the Euclidean space and get a criteria of existence of invariant sets, containing infinite numbers of periodic points. These sets are not structurally stable, but the fact of their existence persists i.e. they may not completely disappear. The applications to vibro-impact systems are considered.|
Room Reservation Information
|Date:||11 / 03 / 2010|
|Time:||03:35pm - 05:05pm|