Study of a transition in the qualitative behaviour of a simple oscillator with Coulomb friction

– (1) Condition (1.1) appearing in the statement of Theorem 1 should be understood as a nonlinear smallness condition on the initial data: the parameter A, measuring through (H1)

After this paper was submitted a paper by Galaktionov, Kurdjumov, Samarskii [7] appeared, which contains part of our results, proved, however, by different

In fact, it is not difficult to verify that all the estimates given in the previous section for the solutions to the Coulomb problem are still valid for the solution to the

As an application, we show that the set of points which are displaced at maximal distance by a “locally optimal” transport plan is shared by all the other optimal transport plans,

Thanks to our result of invertibility of the Jacobian matrix of the flow, we can also prove (Theorem 2 in §4 ) that the process thus defined is a solution to a linear

The basic observation leading to this is that when a contact point is strictly stuck by friction, that means has a reaction strictly inside the Coulomb cone, then the external force

The results are clearly similar to the classical Keller-Segel in two dimensions [6], except that the density converges towards a Dirac mass in the critical case [5].... To prove

The machine learning approach employed is able to recognize with incredible precision the law of evolution of the Duffing oscillator, even with high intensity of noise polluting