Computable Integrability

Аннотация

Already in 19th century Euler and Lagrange established a mathematically satisfactory foundation of Newtonian mechanics. Hamilton developed analogous formulation of optics. Jacobi imported Hamilton's idea in mechanics, and eventually arrived at a new formulation (now referred to as the Hamilton-Jacobi formalism). The Hamilton-Jacobi formalism was a crucial step towards Liouville's classical definition of the notion of integrability. Moreover, Jacobi himself is also famous for having discovered (1839) that the geodesic motion on an ellipsoid is an integrable system which is solvable in terms of hyper-elliptic functions. Jacobi's research on dynamical started in 1837 and deeply motivated by Hamilton's formulation of optics based on the least action. One may say that Hamilton's work played the same role as Abel's work in Jacobi's researches of elliptic functions.