A fractal set of perpetually bouncing universe

关键词: Countable set 、 Physics 、 Classical mechanics 、 Singularity 、 Fractal 、 Set theory 、 Universe (mathematics) 、 Scalar field 、 Aperiodic graph 、 Uncountable set

摘要: For a Friedman-Robertson-Walker universe minimally coupled to massive scalar field, Hawking (1983) has shown that there is countably infinite discrete set of periodic solutions which bounce without singularity. Here it suggested also an uncountably but still perpetually bouncing aperiodic solutions. The latter appears form fractal with positive Hausdorff-Besicovitch dimension.