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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)
In this paper we study the centers of projective vector fields Q T of three-dimensional quasi-homogeneous differential system dx/dt = Q(x) with the weight (m, m, n) and degree 2 on the unit sphere S 2. We seek the sufficient and necessary conditions under which Q T has at least one center on S 2. Moreover, we provide the exact number and the positions of(More)