### Existence of periodic orbits, set of global solutions and behavior near equilibrium for Volterra equations of retarded type.

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The paper presents, mainly, two results: a new proof of the spectral properties of oscillatory matrices and a transversality theorem for diffeomorphisms of R with oscillatory jacobian at every point and such that N(f(x) - f(y)) ≤ N(x - y) for all elements x,y ∈ R, where N(x) - 1 denotes the maximum number of sign changes in the components z of z ∈ R, where all z are non zero and z varies in a small neighborhood of x. An application to a semiimplicit discretization of the scalar heat equation with...

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