Essays about: "ergodic measure"
Found 2 essays containing the words ergodic measure.
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1. A dynamical system with oscillating time average
University essay from Lunds universitet/Matematik LTHAbstract : Given a discrete dynamical system T, one can ask what the time average of the system will be, that is, what is the average position of T^n(x) for large n? Birkhoff’s ergodic theorem, one of the most important results in ergodic theory, says that for an ergodic system on a finite measure space, the time average will in the limit as n -> infinity be equal to the space average for almost all initial values x. In this thesis we study time averages of a dynamical system T : [0, 1] -> [0, 1] that depends on a parameter alpha. READ MORE
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2. Furstenberg's conjecture and measure rigidity for some classes of non-abelian affine actions on tori
University essay from KTH/Matematik (Avd.)Abstract : In 1967 Furstenberg proved that the set {2n3mα(mod 1) | n, m ∈N} is dense in the circle for any irrational α. He also made the following famous measure rigidity conjecture: the only ergodic measures on the circle invariant under both x —> 2x and x —> 3x are the Lebesgue measure and measures supported on a finite set. READ MORE
