Ergodic Theory and Dynamical Systems · 1982 · 110 citations · 2 references
Natural SciencesMathematicsAlgebraGeometryMathematical PhysicsAlgebraic GeometryFixed PointsGroup TheoryInvariant TheoryPeriodic OrbitsGeometric Invariant TheoryInvariant SetsInvariant SubspacesQuasi-periodic Orbits
Abstract A recent result of J. Mather [1] about the existence of quasi-periodic orbits for twist maps is derived from an appropriately modified version of G. D. Birkhoff's classical theorem concerning periodic orbits. A proof of Birkhoff's theorem is given using a simplified geometric version of Mather's arguments. Additional properties of Mather's invariant sets are discussed.
2
CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
Ya. B. Pesin · Russian Mathematical Surveys · 1977 · 1.4K citations