Ergodic Theory and Dynamical Systems · 1988 · 24 citations · 8 references
Natural SciencesMathematicsDynamical SystemsGeometryTopologyEuclidean GeometryInvariant TheoryCircle HomeomorphismsCircle MapsOrbit ClosuresRotationsShadowingShadowing Property
Abstract We define the notions of the pseudo-rotation set and rotation shadowing of pseudo-orbits for endomorphisms of the circle and for homeomorphisms of the annulus. The results include: the rotation shadowing property holds for all endomorphisms of the circle; the pseudo-rotation set equals the closure of the rotation set; the closure of the rotation set varies upper-semicontinuously.
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Non-existence of invariant circles
John N. Mather · Ergodic Theory and Dynamical Systems · 1984 · 145 citations · Full text
Some remarks on Birkhoff and Mather twist map theorems
A. Katok · Ergodic Theory and Dynamical Systems · 1982 · 110 citations · Full text