Mailing address:
Department of Mathematics and Statistics
McGill University
805 Sherbrooke Street West
Montreal, Quebec, H3A 2K6
Canada
Vita
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Research Interests:
KAM Theory, Numerical KAM, Bifurcation Theory, Hyperbolicity, Nonlinear Lattice Equations,
Numerical Analysis, State-Dependent Delay Equations.
My main research interests are in the fields of Dynamical Systems and Mathematical Physics,
in particular in the study of existence and persistence of
invariant objects using Numerical and Analytical tools and their relevance to applications.
I am part of the Applied Mathematics group at McGill.
Publications:
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Calleja, R. and Figueras, J.-Ll.,
Collision of invariant bundles of quasi-periodic attractors in the dissipative standard map,
Chaos 23, 021203 (2012)
preprint: mp_arc
11-182
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Calleja, R. and de la Llave, R., Computation of the breakdown of analyticity in statistical
mechanics models: numerical results and a renormalization group
explanation,
Journal of Statistical Physics (2010) 141:940-951
pdf , preprint:
mp_arc
09-56
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Calleja, R. and de la Llave, R., A numerically accessible criterion for the breakdown
of quasi-periodic solutions and its rigorous justificaition, Nonlinearity 23, (2010) 2029-2058
pdf,
preprint: mp_arc 09-150
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Calleja, R. and Celletti, A., Breakdown of invariant attractors for the
dissipative standard map, Chaos 20, 013121 (2010)
pdf, preprint: mp_arc 09-124
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Calleja, R. and Sire, Y., Travelling waves in discrete nonlinear systems
with non-nearest neighbor interactions,
Nonlinearity 22, (2009) 2583-2605
pdf , preprint: mp_arc 08-188
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Calleja, R. and de la Llave, R.,
Fast numerical computation of quasi-periodic equilibrium states
in 1-D statistical mechanics, including twist maps,
Nonlinearity 22, (2009) 1311-1336
pdf, preprint: mp_arc 08-189
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Lomelí, H.E. and Calleja, R., Heteroclinic bifurcations and chaotic transport
in the two-harmonic Standard-Map, Chaos 16, 023117 (2006)
pdf
Preprints:
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Calleja, R., Doedel, E. J., Humphries, A. R., Lemus-Rodriguez, A., and Oldeman, B. E.,
Computing invariant manifolds and connecting orbits in the Restricted
Three Body Problem,
(accepted for publication in Celestial Mechanics and Dynamical Astronomy), preprint:
arXiv 1111.0032
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Calleja, R., Celletti, A., and de la Llave, R.,
KAM theory for conformally symplectic systems,
(submitted), preprint: mp_arc 11-188
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Calleja, R., Celletti, A., and de la Llave, R.,
Local behavior near quasi-periodic solutions of conformally symplectic systems,
(submitted), preprint: mp_arc 12-16
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Calleja, R., Celletti, A., and de la Llave, R.,
Construction of response functions in forced strongly dissipative systems,
(submitted), preprint: mp_arc 12-79
Theses:
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Existence and persistence of invariant objects in dynamical systems and mathematical physics,
The University of Texas at Austin, Ph.D. Dissertation (May 2009),
Supervisor: Rafael de la Llave.
Frank Gerth III Dissertation Award.
FGDA ,
mp_arc 09-77
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Dinámica simpléctica y approximaciones numéricas de separatrices y
transporte caótico,
Instituto Tecnológico Autónomo de México, B.Sc. Thesis (June 2004),
Supervisor: Hector Lomelí.
In preparation:
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with A. R. Humphries, D. Bernucci, N. Homayounfar, and M. Snarski, Dynamics
of a Singularly Perturbed Delay Differential Equation with Two State-Dependent Delays.
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with A.R. Humphries and N. Christodoulou, Bifurcations and Spurious Solutions for Numerical Methods.
Slides from talks:
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with A.R. Humphries and B. Krauskopf, Invariant Tori in Scalar
State Dependent DDEs.
(Slides form the talk at the ICIAM (Vancouver, July 2011) can be found here)
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with A. Celletti and R. de la Llave, KAM Theory for
Dissipative Systems.
(Slides form the talk at the Fields Institute (Toronto, September 2011) can be found here)
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