Computer Assisted Proof of Drift Orbits Along Normally Hyperbolic Manifolds

Series
CDSNS Colloquium
Time
Friday, February 26, 2021 - 1:00pm for 1 hour (actually 50 minutes)
Location
Zoom (see add'l notes for link)
Speaker
Jorge Gonzalez – Georgia Tech – jgonzalez35@gatech.edu – https://cpb-us-w2.wpmucdn.com/sites.gatech.edu/dist/7/1905/files/2021/02/index.html
Organizer
Alex Blumenthal

Please Note: Zoom link: https://zoom.us/j/97732215148?pwd=Z0FBNXNFSy9mRUx3UVk4alE4MlRHdz09

 

We will discuss a new method for proving the existence of diffusion in some systems with Normally Hyperbolic Invariant Manifolds (NHIM). We apply this approach to the generalized standard map to show the existence of drift orbits for an explicit range of actions.  The method consists of verifying a finite number of conditions on a computer (keywords: NHIM, shadowing, scattering map, Chirikov Standard model, Parameterization Method, Interval Newton Method).