Renato Calleja's Web Page
Mailing
address:
Depto. Matemáticas y Mecánica,
IIMAS
Universidad Nacional Autónoma de México
Admon. No. 20
Delegación Alvaro Obregón
01000 México D.F.
Vita
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.
Animations for the n body
problem
My citations on
Google Scholar
Publications:
- R. Calleja, C. García-Azpeitia, J.P. Lessard, and
J.D. Mireles-James, From the Lagrange polygon to the figure eight I:
Numerical evidence extending a conjecture of Marchal, To appear in Celestial Mech. Dynam. Astronom., preprint:
ArXiv_2012.10759
- R. Calleja, M. Canadell, A. Haro,
Non-twist tori in conformally symplectic systems, Commun. Nonlinear Sci.
Numer. Simul. 96, (2021), 105695,
pdf,
preprint:
ArXiv_2005.09754
- A. P. Bustamante and R. Calleja, Corrigendum and Addendum to "Computation of
domains of analyticity for the dissipative standard map
in the limit of small dissipation", Physica D 417 (2021) 132837,
pdf,
preprint: ArXiv_2010.07500
- R. Calleja, C. García-Azpeitia, J.P. Lessard, and
J.D. Mireles-James, Torus knot choreographies in
the n-body problem, Nonlinearity, Volume 34, Number 1, (2021) 313,
pdf, preprint:
FAU
- Calleja, R., Celletti, A., and de la Llave, R.,
Existence of whiskered KAM tori of conformally
symplectic systems, Nonlinearity, Volume 33, Number 1, (2020) 538–597
pdf, preprint:
ArXiv_1901.07483
- Calleja, R., Celletti, A., and de la Llave, R.,
Whiskered KAM Tori of Conformally Symplectic Systems,
Mathematics Research Reports, Volume 1 (2020), 15-29
pdf
, preprint:
ArXiv_1901.06059
- A. P. Bustamante and R. Calleja, Computation of
domains of analyticity for the dissipative standard map
in the limit of small dissipation, Physica D:
Nonlinear Phenomena, Volume 395, August 2019, Pages 15-23,
pdf , preprint: ArXiv_1712.05476
- R. Calleja, E. Doedel, and C. García-Azpeitia,
Choreographies in the n-vortex problem, Regular and
Chaotic Dynamics, 2018, vol. 23, no. 5, pp. 595-612,
pdf,view only, preprint: ArXiv_1807.08212
- R. Calleja, E. Doedel, C. García-Azpeitia, and Carlos L.
Pando, Choreographies in the Discrete Nonlinear
Schrödinger Equations, Eur. Phys. J. Special Topics
227, 615–624 (2018),
pdf, preprint: ArXiv_1801.03187
- R. Calleja, E. Doedel, and C. García-Azpeitia, Symmetries
and choreographies in families that bifurcate from the
polygonal relative equilibrium of the n-body problem,
Celestial Mech. Dynam. Astronom. 130 (2018), no. 7,
130:48,
pdf, preprint: ArXiv_1702.03990,
animations
- R. Calleja, A. Celletti, R. de la
Llave, Domains of analyticity of Lindstedt
expansions of KAM tori in dissipative perturbations
of Hamiltonian systems, Nonlinearity 30,
(2017) 3151-3202, pdf,
preprint:
mp_arc 15-44
- R. C. Calleja, A. R. Humphries and B. Krauskopf,
Resonance phenomena in a scalar delay differential
equation with two state-dependent delays, SIAM J. Appl. Dyn. Syst.,
16(3),
1474–1513 (2017), pdf,
preprint:
ArXiv_1607.02683
- R. Calleja, D. del-Castillo-Negrete, D.
Martínez-del-Río, and A. Olvera, Global transport in
a nonautonomous standard map, Commun. Nonlinear Sci.
Numer. Simul. 51, October 2017, Pages 198–215,
pdf, preprint:
ArXiv_1601.04824
- R. Calleja, A. Celletti, L. Corsi, R. de la Llave,
Response solutions for quasi-periodic forced,
dissipative wave equations, SIAM J. Math. Anal.,
49(4),
3161–3207 (2017), pdf,
preprint:
ArXiv_1501.05979
- Calleja, R., Doedel, E., and García-Azpeitia, C.,
Symmetry-breaking for a restricted n -body problem in
the Maxwell-ring configuration, Eur. Phys. J.
Special Topics 225, 2741-2750 (2016),
pdf, preprint: ArXiv_1601.06160
- A.R. Humphries, D.A. Bernucci, R. Calleja, N.
Homayounfar and M. Snarski, Periodic Solutions of a
Singularly Perturbed Delay Differential Equation With
Two State-Dependent Delays, J. Dynam. Differential
Equations (2016), Volume 28, Issue 3, pp 1215-1263
pdf, preprint: ArXiv_1411.6060
- D. Martínez, D. del-Castillo-Negrete, A. Olvera, R.
Calleja, Self-consistent chaotic transport in a
high-dimensional mean-field Hamiltonian map model,
Qual. Theory Dyn. Sys. (2015), Volume 14, Issue 2, pp
313-335,
pdf, preprint: ArXiv_1601.00942
- Calleja, R., Celletti, A., Falcolini, C., and de la
Llave, R., An Extension of Greene's Criterion for
Conformally Symplectic Systems and a Partial
Justification, SIAM J. on Mathematical Analysis
(2014), Vol. 46, No. 4, pp 2350-2384,
pdf, preprint:
mp_arc 13-60
- Calleja, R., Celletti, A., and de la Llave, R.,
Local Behavior Near Quasi-Periodic Solutions of
Conformally Symplectic Systems, J. Dynam.
Differential Equations 25 (2013), no. 3, 821-841,
pdf preprint:
mp_arc 12-16
- Calleja, R., Celletti, A., and de la
Llave, R., KAM theory for conformally
symplectic systems: Efficient algorithms and
their validation, J. Differential Equations
255 (2013), no. 5, 978-1049,
pdf preprint:
mp_arc 11-188
- Calleja, R., Celletti, A., and de la Llave, R.,
Construction of response functions in forced strongly
dissipative systems, DCDS-A, Vol. 33 (2013), No. 10,
p. 4411-4433,
pdf preprint:
mp_arc 12-79
- Calleja, R., Doedel, E. J., Humphries, A. R.,
Lemus-Rodriguez, A., and Oldeman, B. E.,
Boundary-value problem formulations for computing
invariant manifolds and connecting orbits in the
circular restricted three body problem, Celestial
Mechanics and Dynamical Astronomy, Volume 114 (2012),
Issue 1-2, pp 77-106
pdf, preprint: ArXiv 1111.0032
- Calleja, R. and Figueras, J.-Ll., Collision of
invariant bundles of quasi-periodic attractors in the
dissipative standard map, Chaos 22, 033114 (2012)
pdf, preprint:
mp_arc 11-182
- 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
- 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
- Calleja, R. and Celletti, A., Breakdown of
invariant attractors for the dissipative standard map,
Chaos 20, 013121 (2010)
pdf, preprint:
mp_arc 09-124
- Calleja, R. and Sire, Y., Travelling waves in
discrete nonlinear systems with non-nearest neighbour
interactions, Nonlinearity 22, (2009) 2583-2605
pdf , preprint:
mp_arc 08-188
- 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
- Lomelí, H.E. and Calleja, R., Heteroclinic
bifurcations and chaotic transport in the two-harmonic
Standard-Map, Chaos 16, 023117 (2006)
pdf
Preprints:
- R. Calleja, A. Celletti, R. de la Llave,
KAM estimates for the dissipative standard map preprint:
ArXiv_2002.10647
- R. Calleja, D. del-Castillo-Negrete, D. Martinez-del-Rio and
A. Olvera,
A new method to compute periodic orbits in general symplectic maps preprint:
ArXiv_2003.02788
- R. Calleja, A. Celletti, R. de la Llave,
KAM theory for some dissipative systems preprint:
ArXiv_2007.08394
Theses:
- 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
- Dinámica simpléctica y approximaciones numéricas de
separatrices y transporte caótico,
Instituto Tecnológico Autónomo de México, B.Sc. Thesis
(June 2004),
Supervisor: Hector Lomelí.
Teaching:
- Sistemas Dinámicos No Lineales
6011
- Mecánica Analítica
IMA
- Sistemas Dinámicos Hamiltonianos
SDH
In preparation:
- with D. Martínez, A. Olvera and D.
del-Castillo-Negrete, Coherent structures in a
high-dimensional self-consistent transport map model