Department of Mathematics
Courant Institute of Mathematical Sciences
New York University
- Email: email@example.com
- Phone: +12405428607
- Office: Warren Weaver Hall, Room 925
Delay coordinate embeddings The delay coordinate embedding method developed by Florens-Takens-Yorke-Casdagli provides a nice embedding of a manifold in R^k and also provides more information about the dyamics underlying the observation time-series. I am currently working with Dr. Dimitris Giannakis on using the properties of this embedding to obtain information on the spectral properties of the dynamical systems.
Mixed-spectrum systems. Dynamical systems whose Koopman operator have a mixed spectrum (continuous and discrete) are said to have mixed spectrum. We are currently studying the foliation in the manifold created by the submersion in Td by the Koopman eigenfunctions.
Escape from almost-invariant sets. In a parameterized family of maps on a manifold, a forward invariant set R with non-empty interior may be created at some critical value of the parameter. Before the parameter attains this critical value, the map is topologically transitive but the average escape time of trajectories from R approaches infinity as the parameter approaches the critical value. I am interested in determining the asymptotic rate at which this quantity approaches infinity. This involves studying how the dynamics of the map determines a Rohlin-tower like structure within the set.
- S Das, J Yorke. Multi-chaos from Quasiperiodicity", SIAM J. App. Dyn.. (2017), to appear
- S Das, Y Saiki, E Sander, J Yorke. Quantitative Quasiperiodicity", Nonlinearity. (2017), to appear
- S Das, et. al. Measuring quasiperiodicity", Europhysics Lett. (2016), 114.4, 40005-40012
- S Das, J Yorke. Quasiperiodicity:Rotation numbers", The Foundations of Chaos Revisited: From Poincare to Recent Advancements (2016), 23-37.
- S Das. Dense saddles in torus maps", Topology Proceedings (2015), 47, 177-190.
- S Das, J Yorke. Avoiding extremes in chaotic systems", J. Diff. Eq. App. (July 2015), 22.2, 217-234.
- S Das, S R Chowdhury, H Saha. Accuracy enhancement in a fuzzy expert decision making system through appropriate determination of membership functions and its application in a medical diagnostic decision making system", Journal of medical systems (2012), 36.3, 1607-1620.