Linear invariant measures for recurrent linear systems
We consider a self-adjoint operator defined by a bidimensional linear system. We extend the Ishii-Pastur-Kotani theory that allows us to identify the absolutely continuous spectrum. From here we deduce that for almost everyE with null Lyapunov exponent the real projective flow admits absolutely continuous invariant measures with square integrable density function.
KeywordsLyapunov Exponent Invariant Measure Rotation Number Exponential Dichotomy Ergodic Measure
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