Abstract We show the equivalences of several notions entropy, like a version topological entropy geodesic flow and Minkowski dimension boundary, in metric spaces with convex bicombings satisfying uniform packing condition. Similar estimates will be given case closed subsets boundary Gromov-hyperbolic bicombings.

We study the closed universe recollapse conjecture for positively curved FRW models with a perfect fluid matter source and a scalar field which arises in the conformal frame of the R+ αR theory. By including ordinary matter, we extend the analysis of a previous work. We analyze the structure of the resulted fourdimensional dynamical system with the methods of the center manifold theory and the ...

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