Topologically Conjugate

Two Maps $\phi,\psi:M\to M$ are said to be topologically conjugate if there Exists a Homeomorphism $h:M\to M$ such that $\phi\circ h=h\circ\psi$, i.e., $h$ maps $\psi$-orbits onto $\phi$-orbits. Two maps which are topologically conjugate cannot be distinguished topologically.

See also Anosov Diffeomorphism