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- Jason D. Mireles-James, Konstantin Mischaikow
- SIAM J. Applied Dynamical Systems
- 2013

This work is concerned with high order polynomial approximation of stable and unstable manifolds for analytic discrete time dynamical systems. We develop a posteriori theorems for these polynomialâ€¦ (More)

- Jan Bouwe van den Berg, Jason D. Mireles-James, Christian Reinhardt
- J. Nonlinear Science
- 2016

We develop techniques for computing the (un)stable manifold at a hyperbolic equilibrium of an analytic vector field. Our approach is based on the so-called parametrization method for invariantâ€¦ (More)

- Jason D. Mireles-James, HÃ©ctor E. LomelÃ
- SIAM J. Applied Dynamical Systems
- 2010

Abstract. Let f : R â†’ R be a diffeomorphism with p0, p1 âˆˆ R distinct hyperbolic fixed points. Assume that W (p0) and W (p1) are two-dimensional manifolds which intersect transversally at a point q.â€¦ (More)

- Jason D. Mireles-James
- J. Nonlinear Science
- 2013

- Roberto Castelli, Jean-Philippe Lessard, Jason D. Mireles-James
- SIAM J. Applied Dynamical Systems
- 2015

We present an efficient numerical method for computing Fourier-Taylor expansions of stable/unstable manifolds associated with hyperbolic periodic orbits. Three features of the method are (1) that weâ€¦ (More)

- Allan Hungria, Jean-Philippe Lessard, Jason D. Mireles-James
- Math. Comput.
- 2016

Judicious use of interval arithmetic, combined with careful pen and paper estimates, leads to effective strategies for computer assisted analysis of nonlinear operator equations. The method of radiiâ€¦ (More)

- Jan Bouwe van den Berg, AndrÃ©a DeschÃªnes, Jean-Philippe Lessard, Jason D. Mireles-James
- SIAM J. Applied Dynamical Systems
- 2015

In this work we introduce a rigorous computational method for finding heteroclinic solutions of a system of two second order differential equations. These solutions correspond to standing wavesâ€¦ (More)

- R. de la Llave, Jason D. Mireles-James
- SIAM J. Applied Dynamical Systems
- 2016

We develop and implement a computer assisted argument for proving the existence of heteroclinic/homoclinic connecting orbits for compact infinite dimensional maps. The argument is based onâ€¦ (More)

- J. L. Gonzalez, Jason D. Mireles-James
- SIAM J. Applied Dynamical Systems
- 2017

We consider the problem of computing stable/unstable manifolds attached to periodic orbits of maps, and develop quasi-numerical methods for polynomial approximation of the manifolds to any desiredâ€¦ (More)

- Maciej J. Capinski, Jason D. Mireles-James
- SIAM J. Applied Dynamical Systems
- 2017

In this work we develop a method for computing mathematically rigorous enclosures of some one dimensional manifolds of heteroclinic orbits for nonlinear maps. Our method exploits a rigorous curveâ€¦ (More)