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oai:recercat.cat:2117/11942025-07-17T06:22:09Zcom_2072_1033col_2072_452950

00925njm 22002777a 4500 dc Delshams Valdés, Amadeu author Gelfreich, Vassili author Jorba, Angel author Martínez-Seara Alonso, M. Teresa author 1996 We consider fast quasiperiodic perturbations of a pendulum with two frequencies $(1,\gamma)$, where $\gamma$ is the golden mean number. For small perturbations such that its Fourier coefficients (the ones associated to Fibonacci numbers), are separated from zero, it is announced that the invariant manifolds split, and the value of the splitting, that turns out to be exponentially small with respect to the perturbation parameter, is correctly predicted by the Melnikov function. An explicit example shows that the splitting can be of the order of some power of $\varepsilon$ if the function $m$ is not analytic. This makes a qualitative difference between periodic and quasiperiodic perturbations Hamiltonian dynamical systems Lagrangian functions Bifurcation theory Hamiltonian systems quasiperiodic forcing Hamilton, Sistemes de Lagrange, Funcions de Bifurcació, Teoria de la Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics Splitting of separatrices for (fast) quasiperiodic forcing