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We study the stability of a scalar inflaton field and analyze its pointattractors in the phase space. We show that the value of the inflaton field inthe vacuum is a bifurcation parameter and prove the possible existence of alimit cycle by using analytical and numerical arguments.Comment: Latex, 11 pages, 3 figures (available upon request), to be published  in Modern Physics Letters

INSTABILITIES, POINT ATTRACTORS AND LIMIT CYCLES IN AN INFLATIONARY UNIVERSE