NYC Dynamics Seminar at CUNY & Yeshiva University is a research level seminar with a broad agenda aimed at research mathematicians and graduate students whose interests include various aspects of the modern theory of dynamical systems and related topics in analysis, geometry, number theory and possibly other subjects. Its aim is to supplement more specialized seminars in the NYC area and provide a meeting place and a venue for discussions for mathematicians associated with various universities and colleges in the NYC metropolitan area working or interested in dynamical systems. The seminar will primarily feature speakers from outside the area specially invited for this purpose as well as mathematicians visiting various NYC universities. Core financial support for the seminar is provided by the Center for Mathematical Sciences at Yeshiva University. Support from other institutions who contribute to funding visits of seminar speakers will be acknowledged.
Both locations require participants to present some form of identification to the security to be signed in.
Meeting Times: We plan to meet roughly every other Wednesday at 5pm for the Fall, 2016 semester. We will alternate locations between the CUNY Graduate Center and Yeshiva University. The typical lecture time will be 1 hour, followed by a short period for questions or discussions.
We present a Melnikov type approach for establishing transversal intersections of stable/unstable manifolds of perturbed normally hyperbolic invariant manifolds. In our approach, we do not need to know the explicit formulas for the homoclinic orbits prior to the perturbation. We also do not need to compute any integrals along such homoclinics. All needed bounds are established using rigorous computer assisted numerics. Lastly, and most importantly, the method establishes intersections for an explicit range of parameters, and not only for perturbations that are ‘small enough’, as is the case in the classical Melnikov approach.
I will describe a recent observation which shows that Gaussian curvature plays a key role in the gyroscopic effect, and in particular in the the dynamics of the Lagrange top. In addition, I will show some other examples exhibiting unexpected magnetic—like or gyroscopic—like effects. This talk is based on joint work with Graham Cox.