We prove that every orientation-preserving periodic self-homeomorphism f of a 2-dimen-sional orientable closed manifold M can be resolved into several basic periodic motions.From this it follows that the number of sho...We prove that every orientation-preserving periodic self-homeomorphism f of a 2-dimen-sional orientable closed manifold M can be resolved into several basic periodic motions.From this it follows that the number of shorter-periodic orbits of f does not. exceed 2+min{4q,24q/m} (where m is the period of f, and q is the genus of M). When q>1, the periodof f is not greater than 4q+2. Moreover, we prove that the number of topologically conju-gate classes of orientation-preserving periodic self-homeomorphisms on M is finite if q>1.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘We prove that every orientation-preserving periodic self-homeomorphism f of a 2-dimen-sional orientable closed manifold M can be resolved into several basic periodic motions.From this it follows that the number of shorter-periodic orbits of f does not. exceed 2+min{4q,24q/m} (where m is the period of f, and q is the genus of M). When q>1, the periodof f is not greater than 4q+2. Moreover, we prove that the number of topologically conju-gate classes of orientation-preserving periodic self-homeomorphisms on M is finite if q>1.
