Orbital behaviour transition from the Henon-Heiles to the three-particle Toda lattice Hamiltonian
For the n-order approximations \(H_ n\) of the three particle Toda lattice, plots of orbits on sections and of Lyapunov exponents of periodic orbits are presented for \(n\leq 3\leq 10\), and for the standard homotopy \(\epsilon \mapsto H_{34}(\epsilon)\) between \(H_ 3\) and \(H_ 4\), \(H_{34}(\epsilon)=H_ 3+\epsilon (H_ 4-H_ 3)\), \(0\leq \epsilon \leq 1\), at various energy levels. These plots are discussed in detail, directing attention to (perceptible) transitions from regular to chaotic behaviour.
scientific article; zbMATH DE number 4160203