What does it mean for an orbit to "accumulate"? For example, from Beardon's "A Primer On Riemann Surfaces", > ...Show that g is a homeomorphism of D onto itself, and that no orbit accumulates in D. I'm simply looking for a definition of the word accumulates; I haven't encountered it yet and he presents no formal meaning previously.

Very roughly, it is saying something like that the orbit should not have a subsequence with a Limit Point. That wiki page contains various definitions related to accumulation points in a topological space. The specific one given is:


"A point x ∈ X is a cluster point or accumulation point of a sequence
(xn)n ∈ N if, for every neighbourhood V of x, there are infinitely many
natural numbers n such that xn ∈ V."