39 citations · 163 across the 22 of their papers we have counts for
26 papers
Biological network dynamics: Poincaré-Lindstedt series and the effect of delays
Renato Calleja, Pablo Padilla-Longoria, Edgar Rodríguez-Mendieta
This paper focuses on the Hopf bifurcation in an activator-inhibitor system without diffusion which can be modeled as a delay differential equation. The main result of this paper i…
From the Lagrange Triangle to the Figure Eight Choreography: Proof of Marchal's Conjecture
Renato Calleja, Carlos García-Azpeitia, Olivier Hénot +2
For the three body problem with equal masses, we prove that the most symmetric continuation class of Lagrange's equilateral triangle solution, also referred to as the fami…
Accurate computations up to break-down of quasi-periodic attractors in the dissipative spin-orbit problem
Renato Calleja, Alessandra Celletti, Joan Gimeno +1
We consider a Celestial Mechanics model: the spin-orbit problem with a dissipative tidal torque, which is a singular perturbation of a conservative system. The goal of this paper i…
KAM quasi-periodic tori for the dissipative spin-orbit problem
Renato Calleja, Alessandra Celletti, Joan Gimeno +1
We provide evidence of the existence of KAM quasi-periodic attractors for a dissipative model in Celestial Mechanics. We compute the attractors extremely close to the breakdown thr…
Efficient and accurate KAM tori construction for the dissipative spin-orbit problem using a map reduction
Renato Calleja, Alessandra Celletti, Joan Gimeno +1
We consider the dissipative spin-orbit problem in Celestial Mechanics, which describes the rotational motion of a triaxial satellite moving on a Keplerian orbit subject to tidal fo…
From the Lagrange polygon to the figure eight I: Numerical evidence extending a conjecture of Marchal
Renato Calleja, Carlos García-Azpeitia, Jean-Philippe Lessard +1
The present work studies the continuation class of the regular -gon solution of the -body problem. For odd numbers of bodies between and we apply one paramet…
Corrigendum and Addendum to "Computation of domains of analyticity for the dissipative standard map in the limit of small dissipation" [arXiv:1712.05476]
Adrian P. Bustamante, Renato C. Calleja
We correct some tables and figures in [A.P. Bustamante and R.C. Calleja, Physica D: Nonlinear Phenomena, 395 (2019), pp. 15-23, arXiv:1712.05476]. We also report on the new computa…
KAM theory for some dissipative systems
Renato Calleja, Alessandra Celletti, Rafael de la Llave
Dissipative systems play a very important role in several physical models, most notably in Celestial Mechanics, where the dissipation drives the motion of natural and artificial sa…
Non-twist tori in conformally symplectic systems
Renato Calleja, Marta Canadell, Alex Haro
Dissipative mechanical systems on the torus with a friction that is proportional to the velocity are modeled by conformally symplectic maps on the annulus, which are maps that tran…
A new method to compute periodic orbits in general symplectic maps
Renato Calleja, Diego del-Castillo-Negrete, David Martinez-del-Rio +1
The search of high-order periodic orbits has been typically restricted to problems with symmetries that help to reduce the dimension of the search space. Well-known examples includ…
KAM estimates for the dissipative standard map
Renato Calleja, Alessandra Celletti, Rafael de la Llave
From the beginning of KAM theory, it was realized that its applicability to realistic problems depended on developing quantitative estimates on the sizes of the perturbations allow…
Whiskered KAM Tori of Conformally Symplectic Systems
Renato C. Calleja, Alessandra Celletti, Rafael de la Llave
We investigate the existence of whiskered tori in some dissipative systems, called \sl conformally symplectic \rm systems, having the property that they transform the symplectic fo…
Existence of whiskered KAM tori of conformally symplectic systems
Renato C. Calleja, Alessandra Celletti, Rafael de la Llave
We study the existence of whiskered tori in a family of conformally symplectic maps depending on parameters . Whiskered tori are tori on which the motion is a rotation, bu…
Torus knot choreographies in the -body problem
Renato Calleja, Carlos García-Azpeitia, Jean-Philippe Lessard +1
We develop a systematic approach for proving the existence of choreographic solutions in the gravitational body problem. Our main focus is on spatial torus knots: that is, peri…
Choreographies in the -vortex problem
Renato Calleja, Eusebius Doedel, Carlos García-Azpeitia
We consider the equations of motion of vortices of equal circulation in the plane, in a disk and on a sphere. The vortices form a polygonal equilibrium in a rotating frame of r…
Choreographies in the Discrete Nonlinear Schrödinger Equations
Renato Calleja, Eusebius Doedel, Carlos García-Azpeitia +1
We study periodic solutions of the discrete nonlinear Schrödinger equation (DNLSE) that bifurcate from a symmetric polygonal relative equilibrium containing sites. With special…
Computation of Domains of Analyticity for the dissipative standard map in the limit of small dissipation
Adrian P. Bustamante, Renato C. Calleja
Conformally symplectic systems include mechanical systems with a friction proportional to the velocity. Geometrically, these systems transform a symplectic form into a multiple of…
Symmetries and choreographies in families bifurcating from the polygonal relative equilibrium of the -body problem
Renato Calleja, Eusebius Doedel, Carlos García-Azpeitia
We use numerical continuation and bifurcation techniques in a boundary value setting to follow Lyapunov families of periodic orbits. These arise from the polygonal system of bo…
Resonance phenomena in a scalar delay differential equation with two state-dependent delays
R. C. Calleja, A. R. Humphries, B. Krauskopf
We study a scalar DDE with two delayed feedback terms that depend linearly on the state. The associated constant-delay DDE, obtained by freezing the state dependence, is linear and…
Global transport in a nonautonomous standard map
Renato Calleja, Diego del-Castillo-Negrete, David Martinez-del-Rio +1
A non-autonomous version of the standard map with a periodic variation of the parameter is introduced and studied. Symmetry properties in the variables and parameters of the map ar…
Self-consistent chaotic transport in a high-dimensional mean-field Hamiltonian map model
D. Martínez-del-Río, D. del-Castillo-Negrete, A. Olvera +1
Self-consistent chaotic transport is studied in a Hamiltonian mean-field model. The model provides a simplified description of transport in marginally stable systems including vort…
Symmetry-breaking for a restricted n-body problem in the Maxwell-ring configuration
Renato Calleja, Eusebius Doedel, Carlos García-Azpeitia
We investigate the motion of a massless body interacting with the Maxwell relative equilibrium, which consists of n bodies of equal mass at the vertices of a regular polygon that r…
Domains of analyticity of Lindstedt expansions of KAM tori in dissipative perturbations of Hamiltonian systems
Renato C. Calleja, Alessandra Celletti, Rafael de la Llave
Many problems in Physics are described by dynamical systems that are conformally symplectic (e.g., mechanical systems with a friction proportional to the velocity, variational prob…
Response solutions for quasi-periodically forced, dissipative wave equations
Renato C. Calleja, Alessandra Celletti, Livia Corsi +1
We consider several models of nonlinear wave equations subject to very strong damping and quasi-periodic external forcing. This is a singular perturbation, since the damping is not…