1 citations · 1 across the 3 of their papers we have counts for
5 papers
Coupled cell networks and their hidden symmetries
Bob Rink, Jan Sanders
Dynamical systems with a coupled cell network structure can display synchronous solutions, spectral degeneracies and anomalous bifurcation behavior. We explain these phenomena here…
Amplified Hopf bifurcations in feed-forward networks
Bob Rink, Jan Sanders
In a previous paper, the authors developed a method for computing normal forms of dynamical systems with a coupled cell network structure. We now apply this theory to one-parameter…
Coupled cell networks: semigroups, Lie algebras and normal forms
Bob Rink, Jan Sanders
We introduce the concept of a semigroup coupled cell network and show that the collection of semigroup network vector fields forms a Lie algebra. This implies that near a dynamical…
Proof of Nishida's conjecture on anharmonic lattices
Bob Rink
We prove Nishida's 1971 conjecture stating that almost all low-energetic motions of the anharmonic Fermi-Pasta-Ulam lattice with fixed endpoints are quasi-periodic. The proof is ba…
A Cantor set of tori with monodromy near a focus-focus singularity
B. Rink
We write down an asymptotic expression for action coordinates in an integrable Hamiltonian system with a focus-focus equilibrium. From the singularity in the actions we deduce that…