Adaptive Set-Oriented Computation of Topological Horseshoe Factors in Area and Volume Preserving Maps. - Jason D. Mireles-James (SIAM J. Appl. Dyn. Syst., 2010)

Computation of Heteroclinic Arcs with Application to the Volume Preserving Hénon Family. - Jason D. Mireles-James; Héctor E. Lomelí (SIAM J. Appl. Dyn. Syst., 2010)

Rigorous Numerics for Symmetric Connecting Orbits: Even Homoclinics of the Gray-Scott Equation. - Jan Bouwe van den Berg; Jason D. Mireles-James; Jean-Philippe Lessard; Konstantin Mischaikow (SIAM J. Math. Anal., 2011)

Quadratic Volume-Preserving Maps: (Un)stable Manifolds, Hyperbolic Dynamics, and Vortex-Bubble Bifurcations. - Jason D. Mireles-James (J. Nonlinear Sci., 2013)

Rigorous A Posteriori Computation of (Un)Stable Manifolds and Connecting Orbits for Analytic Maps. - Jason D. Mireles-James; Konstantin Mischaikow (SIAM J. Appl. Dyn. Syst., 2013)

Computer assisted error bounds for linear approximation of (un)stable manifolds and rigorous validation of higher dimensional transverse connecting orbits. - Jason D. Mireles-James (Commun. Nonlinear Sci. Numer. Simul., 2015)

Stationary Coexistence of Hexagons and Rolls via Rigorous Computations. - Jan Bouwe van den Berg; Andréa Deschênes; Jean-Philippe Lessard; Jason D. Mireles-James (SIAM J. Appl. Dyn. Syst., 2015)

Parameterization of Invariant Manifolds for Periodic Orbits I: Efficient Numerics via the Floquet Normal Form. - Roberto Castelli; Jean-Philippe Lessard; Jason D. Mireles-James (SIAM J. Appl. Dyn. Syst., 2015)

Computing (Un)stable Manifolds with Validated Error Bounds: Non-resonant and Resonant Spectra. - Jan Bouwe van den Berg; Jason D. Mireles-James; Christian Reinhardt (J. Nonlinear Sci., 2016)

Rigorous numerics for analytic solutions of differential equations: the radii polynomial approach. - Allan Hungria; Jean-Philippe Lessard; Jason D. Mireles-James (Math. Comput., 2016)

Connecting Orbits for Compact Infinite Dimensional Maps: Computer Assisted Proofs of Existence. - Rafael de la Llave; Jason D. Mireles-James (SIAM J. Appl. Dyn. Syst., 2016)

High-order parameterization of (un)stable manifolds for hybrid maps: Implementation and applications. - Vincent Naudot; Jason D. Mireles-James; Qiuying Lu (Commun. Nonlinear Sci. Numer. Simul., 2017)

Fourier-Taylor Approximation of Unstable Manifolds for Compact Maps: Numerical Implementation and Computer-Assisted Error Bounds. - Jason D. Mireles-James (Found. Comput. Math., 2017)

Chebyshev-Taylor Parameterization of Stable/Unstable Manifolds for Periodic Orbits: Implementation and Applications. - Jason D. Mireles-James; Maxime Murray (Int. J. Bifurc. Chaos, 2017)

Validated Computation of Heteroclinic Sets. - Maciej J. Capinski; Jason D. Mireles-James (SIAM J. Appl. Dyn. Syst., 2017)

High-Order Parameterization of Stable/Unstable Manifolds for Long Periodic Orbits of Maps. - J. L. Gonzalez; Jason D. Mireles-James (SIAM J. Appl. Dyn. Syst., 2017)

Computer Assisted Fourier Analysis in Sequence Spaces of Varying Regularity. - Jean-Philippe Lessard; Jason D. Mireles-James (SIAM J. Math. Anal., 2017)

Analytic Continuation of Local (Un)Stable Manifolds with Rigorous Computer Assisted Error Bounds. - William D. Kalies; Shane Kepley; Jason D. Mireles-James (SIAM J. Appl. Dyn. Syst., 2018)

Resonant tori, transport barriers, and chaos in a vector field with a Neimark-Sacker bifurcation. - Emmanuel Fleurantin; Jason D. Mireles-James (Commun. Nonlinear Sci. Numer. Simul., 2020)

Parameterization Method for Unstable Manifolds of Standing Waves on the Line. - Blake Barker; Jason D. Mireles-James; Jalen Morgan (SIAM J. Appl. Dyn. Syst., 2020)

Computer assisted proof of drift orbits along normally hyperbolic manifolds. - Maciej J. Capinski; Jorge Gonzalez; Jean-Pierre Marco; Jason D. Mireles-James (Commun. Nonlinear Sci. Numer. Simul., 2022)

Computer assisted proofs in dynamical systems. - Maciej J. Capinski; Jason D. Mireles-James; Warwick Tucker; Daniel Wilczak; Jan Bouwe van den Berg (Commun. Nonlinear Sci. Numer. Simul., 2023)

Persistence of Periodic Orbits under State-dependent Delayed Perturbations: Computer-assisted Proofs. - Joan Gimeno; Jean-Philippe Lessard; Jason D. Mireles-James; Jiaqi Yang (SIAM J. Appl. Dyn. Syst., 2023)

Numerical Computation of Transverse Homoclinic Orbits for Periodic Solutions of Delay Differential Equations. - Olivier Hénot; Jean-Philippe Lessard; Jason D. Mireles-James (SIAM J. Appl. Dyn. Syst., 2023)

Computer assisted proofs for transverse heteroclinics by the parameterization method. - Maxime Murray; Jason D. Mireles-James (CoRR, 2024)

Weighted Birkhoff Averages and the Parameterization Method. - David Blessing; Jason D. Mireles-James (SIAM J. Appl. Dyn. Syst., 2024)

State Dependent Delay Maps: Numerical Algorithms and Dynamics of Projections. - Jason D. Mireles-James; Francis C. Motta; Vincent Naudot (Exp. Math., 2025)