46 citations · 173 across the 9 of their papers we have counts for
9 papers
Pattern formation in coiling of falling viscous threads: Revisiting the geometric model
Will Sze, Eusebius J. Doedel, Ida Karimfazli +1
The "Fluid Mechanic Sewing Machine" creates periodic patterns through the coiling nature of a viscous fluid falling onto a moving surface. At relatively moderate heights, the repor…
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…
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…
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…
Computing Invariant Manifolds and Connecting Orbits in the Circular Restricted Three Body Problem
Renato C. Calleja, Eusebius J. Doedel, Antony R. Humphries +2
We demonstrate the remarkable effectiveness of boundary value formulations coupled to numerical continuation for the computation of stable and unstable manifolds in systems of ordi…
Continuation of connecting orbits in 3D-ODEs: (II) Cycle-to-cycle connections
E. J. Doedel, B. W. Kooi, Yu. A. Kuznetsov +1
In Part I of this paper we discussed new methods for the numerical continuation of point-to-cycle connecting orbits in 3-dimensional autonomous ODE's using projection boundary cond…
Continuation of connecting orbits in 3D-ODEs: (I) Point-to-cycle connections
E. J. Doedel, B. W. Kooi, Yu. A. Kuznetsov +1
We propose new methods for the numerical continuation of point-to-cycle connecting orbits in 3-dimensional autonomous ODE's using projection boundary conditions. In our approach, t…
Successive Continuation for Locating Connecting Orbits
E. J. Doedel, M. J. Friedman, B. I. Kunin
A successive continuation method for locating connecting orbits in parametrized systems of autonomous ODEs is considered. A local convergence analysis is presented and several illu…