Resumen de Three families of isochrone-type canonical transformations

Sebastián Ferrer Martínez , Martín Lara Coira

• Hénon’s isochrone Hamiltonian is formulated in extended phase space including a time transformation. Then, the Hamilton-Jacobi equation a la Poincar´e is used to find suitable canonical transformations that reduces the original Hamiltonian to a function of only the momenta. We focus on three different time transformations, for each of which we build a family of canonical transformations where the new Hamiltonian remains unspecified. Materialization of particular transformations based on specific requirements lead to a partial differential equation which the new Hamiltonian ought to satisfy. Specifically, we show how different canonical transformations in the Literature may be recovered from our families.