ABSTRACT

Title:  An Iterated Symplectic Map for Understanding Hamiltonian Chaos

PI: Dr Mitaxi Mehta

Funding Organization: Science and Engineering Research Board (SERB)

Duration: 3 years 

Summary:-   Hamiltonian Chaos has characteristic tangle of periodic orbits and corresponding scaling behavior as a non linearity parameter is varied. While scaling of such periodic orbits is well understood in one dimensional maps. The scaling of orbits in Hamiltonian systems is much more challenging and complex due to bifurcations of multiple orbits at the same time. The project will attempt to do the following,

(1)  Construct the symplectic maps that map momenta from one symmetry line to another,  numerically,on an energy surface and find approximate analytical expressions using curve fitting.  Use linear and nonlinear regression methods for the purpose. 

(2) Look for symbolic dynamics rules that decide how iterations from one branch of the surface to another are carried out. Look for feasibility of pictorial iteration schemes like the logistic map. 

(3) Study the change in the shape of the surfaces defined by the maps numerically as epsilon (or energy) is changed and attempt to model that change. Make use of regression techniques. If a good model can be identified study bifurcationcascade in the model. 

(4) Continue previous study. Study various geometric representations of iterations of the map, along projections as well as in 3D.

Keywords: Funded Research