Renato Calleja's Web Page
      Renato C. Calleja             
              Investigador Titular A (Associate Professor)
              Department of Mathematics and Mechanics
              IIMAS- UNAM     
         E-mail:  calleja(at)mym(dot)iimas(dot)unam(dot)mx

         Office: IIMAS 222

Computer assisted proofs in Nonlinear Dynamics Course

Mailing address:
Depto. Matemáticas y Mecánica, IIMAS  
Universidad Nacional Autónoma de México  
Admon. No. 20  
Delegación Alvaro Obregón  
01000 México D.F.


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

  1. R. Calleja, C. García-Azpeitia, J.P. Lessard, and J.D. Mireles-James, Torus knot choreographies in the n-body problem, Accepted for publication in Nonlinearity (2020), preprint: FAU

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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
  20. 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

  21. 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

  22. 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

  23. Calleja, R. and Celletti, A., Breakdown of invariant attractors for the dissipative standard map, Chaos 20, 013121 (2010)
    pdf, preprint: mp_arc 09-124

  24. 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

  25. 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

  26. Lomelí, H.E. and Calleja, R., Heteroclinic bifurcations and chaotic transport in the two-harmonic Standard-Map, Chaos 16, 023117 (2006)
    1. R. Calleja, A. Celletti, R. de la Llave, KAM estimates for the dissipative standard map preprint: ArXiv_2002.10647

    2. 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

    3. R. Calleja, M. Canadell, A. Haro, Non-twist tori in conformally symplectic systems preprint: ArXiv_2005.09754

    4. R. Calleja, A. Celletti, R. de la Llave, KAM theory for some dissipative systems preprint: ArXiv_2007.08394

    5. 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", preprint: ArXiv_2010.07500

  • 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.
  • Sistemas Dinámicos No Lineales 6011
  • Mecánica Analítica IMA
In preparation:
  • with D. Martínez, A. Olvera and D. del-Castillo-Negrete, Coherent structures in a high-dimensional self-consistent transport map model