Abstract: We study when a compact group of homeomorphisms of the
closed unit three-ball B can be either
finite or topologically equivalent to a subgroup oftheorthogonalgroupWealsotopologicallycharacterizepositively
equicontinuous flows on B and
equicontinuous flows on having
bounded orbits.
Keywords and phrases: compact group of homeomorphisms of the unit three-ball, Lie group, equicontinuous flow, topologically equivalent.