On orbits of the same type (Q1270586)

The author considers the following situation: \(X\) is a Hausdorff uniform space, \(f:X\to X\) is a continuous bijection, \(A\subset X\) is connected, invariant and Lyapunov stable and for every \(x\in A\), the closure of the orbit of \(x\) is homeomorphic to the circle. The author studies the corresponding rotation numbers. Among others, assumptions are found under which the rotation number is constant on \(A\). Some examples and related results are added.