3 papers
math.DS2025
A Practical Guide to Rigorously Locate Periodic Orbits in Discrete Dynamics
Lucía Alonso Mozo, Olivier Hénot, Phillipo Lappicy
Periodic orbits are important objects of discrete dynamical systems, but finding them is not always easy. We present a self-contained introductory account, aimed at non-experts, to…
math.DS2025
Global Continuation of Stable Periodic Orbits in Systems of Competing Predators
Kevin E. M. Church, Jia-Yuan Dai, Olivier Hénot +2
We develop a continuation technique to obtain global families of stable periodic orbits, delimited by transcritical bifurcations at both ends. To this end, we formulate a zero-find…
math.DS2024
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…