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We study the closed universe recollapse conjecture for positively curved FRWmodels with a perfect fluid matter source and a scalar field which arises inthe conformal frame of the $R+\alpha R^{2}$ theory. By including ordinarymatter, we extend the analysis of a previous work. We analyze the structure ofthe resulted four-dimensional dynamical system with the methods of the centermanifold theory and the normal form theory. It is shown that an initiallyexpanding closed FRW universe, starting close to the Minkowski spacetime,cannot avoid recollapse. We discuss the posibility that potentials with apositive minimum may prevent the recollapse of closed universes.Comment: 15 pages, 3 figures, submitted to JM

The recollapse problem of closed Friedmann–Robertson–Walker models in higher-order gravity theories