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Vanishing Stochastic Perturbations of
Hamiltonian Systems
CASA Day, Nov 2013
Work with M. Hong Duong and Mark Peletier
Upanshu Sharma
“It has been said that something as small as the flutter
of a butterfly's wing can ultimately cause a typhoon
halfway around the world.”
-The Butterfly Effect
1
Toy Problem
2
Toy Problem
2
Toy Problem
2
Hamiltonian – Conserved Quantity
3
Celestial Mechanics
Magnetic Traps
etc…
Hamiltonian – Conserved Quantity
3
Problem
4
What are the dynamics
as ?
Problem
4
SDE to PDE
5
Diffusion on a Graph
6
In the limit :
Diffusion on a Graph
6
Show me the MATH !
7
Show me the MATH !
7
Result…
8
• x\
• A
• C
Conclusions
9
Result…
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