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

         Office: IIMAS 226

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.

My citations on Google Scholar


Publications:
  • 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., 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., 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:
  • Calleja, R., Celletti, A., Falcolini, C., and de la Llave, R., A partial justification of Greene's criterion for confromally symplectic systems, submitted for publication, preprint: mp_arc 13-60

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.
In preparation:
  • Efficient computation of periodic orbits in Hamiltonian systems

  • with A. R. Humphries, D. Bernucci, N. Homayounfar, and M. Snarski, Dynamics of a singularly perturbed delay differential equation with two state-dependent delays.

Slides from talks:
  • 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)

  • 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)