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Jay Mireles James
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Rigorous numerics for symmetric connecting orbits: Even homoclinics of the Gray–Scott equation
JB van den Berg, JD Mireles-James, JP Lessard, K Mischaikow
SIAM Journal on Mathematical Analysis 43 (4), 1557-1594, 2011
982011
Rigorous numerics for analytic solutions of differential equations: the radii polynomial approach
A Hungria, JP Lessard, J Mireles James
Mathematics of Computation 85 (299), 1427-1459, 2016
932016
Computing (un) stable manifolds with validated error bounds: non-resonant and resonant spectra
JB van den Berg, JD Mireles James, C Reinhardt
Journal of Nonlinear Science 26, 1055-1095, 2016
732016
Computer assisted proof of transverse saddle-to-saddle connecting orbits for first order vector fields
JP Lessard, JD Mireles James, C Reinhardt
Journal of Dynamics and Differential Equations 26, 267-313, 2014
702014
Parameterization of invariant manifolds for periodic orbits I: Efficient numerics via the Floquet normal form
R Castelli, JP Lessard, JD Mireles James
SIAM Journal on Applied Dynamical Systems 14 (1), 132-167, 2015
692015
Rigorous a posteriori computation of (un) stable manifolds and connecting orbits for analytic maps
JD Mireles James, K Mischaikow
SIAM Journal on Applied Dynamical Systems 12 (2), 957-1006, 2013
662013
Stationary coexistence of hexagons and rolls via rigorous computations
JB van den Berg, A Deschênes, JP Lessard, JD Mireles James
SIAM Journal on Applied Dynamical Systems 14 (2), 942-979, 2015
632015
Computation of maximal local (un) stable manifold patches by the parameterization method
M Breden, JP Lessard, JDM James
Indagationes Mathematicae 27 (1), 340-367, 2016
592016
Automatic differentiation for Fourier series and the radii polynomial approach
JP Lessard, JDM James, J Ransford
Physica D: Nonlinear Phenomena 334, 174-186, 2016
572016
Computation of heteroclinic arcs with application to the volume preserving Hénon family
JDM James, H Lomelí
SIAM Journal on Applied Dynamical Systems 9 (3), 919-953, 2010
522010
Quadratic volume-preserving maps:(un) stable manifolds, hyperbolic dynamics, and vortex-bubble bifurcations
JD Mireles James
Journal of Nonlinear Science 23, 585-615, 2013
452013
Polynomial approximation of one parameter families of (un) stable manifolds with rigorous computer assisted error bounds
JDM James
Indagationes Mathematicae 26 (1), 225-265, 2015
422015
Parameterization method for unstable manifolds of delay differential equations
CM Groothedde, JDM James
Journal of Computational Dynamics 4 (1&2), 21-70, 2017
392017
Fourier–Taylor parameterization of unstable manifolds for parabolic partial differential equations: formalism, implementation and rigorous validation
C Reinhardt, JDM James
Indagationes Mathematicae 30 (1), 39-80, 2019
352019
Validated numerics for equilibria of analytic vector fields: invariant manifolds and connecting orbits
JDM James
Rigorous numerics in dynamics 74, 27-80, 2017
302017
Chebyshev–Taylor parameterization of stable/unstable manifolds for periodic orbits: implementation and applications
JD Mireles James, M Murray
International Journal of Bifurcation and Chaos 27 (14), 1730050, 2017
292017
Chebyshev–Taylor parameterization of stable/unstable manifolds for periodic orbits: implementation and applications
JD Mireles James, M Murray
International Journal of Bifurcation and Chaos 27 (14), 1730050, 2017
292017
Parameterization of slow-stable manifolds and their invariant vector bundles: theory and numerical implementation
JB van den Berg, JDM James
Discrete Contin. Dyn. Syst 36 (9), 4637-4664, 2016
292016
Parameterization of invariant manifolds by reducibility for volume preserving and symplectic maps
R de la Llave, JDM James
Discrete Contin. Dyn. Syst 32 (12), 4321-4360, 2012
292012
Parameterization of invariant manifolds for periodic orbits (II): A posteriori analysis and computer assisted error bounds
R Castelli, JP Lessard, JDM James
Journal of Dynamics and Differential Equations 30, 1525-1581, 2018
282018
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