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Dr. Jason Mireles-James

Dr. Rindy Anderson
  • Assistant Professor
  • Department of Mathematical Sciences
  • 561-297-2490
  • jmirelesjames@fau.edu
  • Boca Raton - SE43, Room 262

Education

  • Ph.D. Mathematics. University of Texas at Austin. December 2009

Research Interests

  • Computational Topology in Dynamical Systems: Conley Index Theory, Set Oriented Numerics, computational aspects of Morse/Floer theory, and Applications.
  • A Posteriori Analysis and Numerics in Dynamical Systems: Parameterization of invariant manifolds with rigorous error bounds. Applications to computer assisted proof of connecting dynamics for diffeomorphisms, ordinary and partial differential equations.
  • KAM Theory: existence and numerical approximation of invariant manifolds in spite of small divisors.

Research Description

  • The computer as the mathematician's "laboratory" for studying global dynamics of nonlinear systems. I'm especially interested in the computation and visualization of smooth invariant manifolds.
  • Reformulation of qualitative questions about nonlinear dynamical systems into quantitative functional equations, and numerical methods for studying these functional equations.
  • Rigorous numerical methods and computer assisted proof in analysis, especially constructive a-posteriori existence (or "shadowing") theorems for invariant manifolds, connecting dynamics, and chaotic motions.

Recent Publications

  • Analytic continuation of local (un)stable manifolds with rigorous computer assisted error bounds.''   With Shane Kepley and Bill Kalies. SIAM Journal on Applied Dynamical Systems, Vol 17, No. 1, pp. 157--202 (2018)
  • Chebyshev-Taylor parameterization of stable/unstable manifolds for periodic orbits: implementation and applications.'' With Maxime Murray. International Journal of Bifurcation and Chaos, Vol 27, No. 14 (2017).

Scholarly Activities

Personal Website

http://brain2.math.fau.edu/~jmirelesjames/index.html

 

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