For a given family of planar differential equations it is a very difficult problem to determine an upper bound for the number of its limit cycles. Even when this upper bound is one it is not always an easy problem to distinguish between the case of zero and one limit cycle. This note mainly deals with this second problem for a family of systems with a… (More)
Let / : M —» M be a C1 map on a C1 differentiate manifold. The map f is called transversal if for all m £ N the graph of fm intersects transversally the diagonal of M x M at each point (x, x) such that x is a fixed point of fm. We study the set of periods of / by using the Lefschetz numbers for periodic points. We focus our study on transversal maps defined… (More)
We consider a system of the form ˙ We prove that this system has at most one limit cycle and that when it exists it can be explicitly found. Then we study a particular case, with n = 3 and m = 4. We prove that this quintic polynomial system has an explicit limit cycle which is not algebraic. To our knowledge, there are no such type of examples in the… (More)
Dado un cero de una aplicacii on anal tica f de R n en si mismo, Eisenbud y Levine dan una cota para el ndice de f en este punto a partir de su multiplicidad. En este trabajo se demuestra que esta cota es optima para el caso n = 2, y que se puede mejorar para dimensii on superior.