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We give a short discussion about a weaker form of minimality (calledquasi-minimality). We call a system quasi-minimal if all dense orbits form anopen set. It is hard to find examples which are not already minimal. Sinceelliptic behaviour makes them minimal, these systems are regarded as parabolicsystems. Indeed, we show that a quasi-minimal homeomorphism on a manifold isnot expansive (hyperbolic).

Quasi-Minimal, Pseudo-Minimal Systems and Dense Orbits