topological conjugacy
A homeomorphism intertwining two evolution maps transports their orbit structure. Use the defining commuting equation to track periodic points and transitivity, and distinguish this equivalence from a noninvertible factor map.
Before opening the references
homeomorphism · Orbit of a Dynamical System · Topological Transitivity
Where to read
Start here: Ordinary Differential Equations and Dynamical Systems (author's preliminary version)
Gerald Teschl · Book · English · Free full text
§11.3 On the definition of chaos, equation (11.10) and the following discussion of periodic points and transitivity, printed p. 296
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Dynamical Systems & Ergodic Theory in the library · Preparation and skip guidance · Terminology and translation evidence