Add to ORKGIt has been established one-side uniform convergence in both the Birkhoff and sub-additive ergodic theorems under conditions on growth rates with respect to all the invariant measures. In this paper we show these conditions are both necessary and sufficient. These results are applied to study quasiperiodically forced systems. Some meaningful geometric properties of invariant sets of such systems are presented. We also show that any strange compact invariant set of a C-1 quasiperiodically forced system must support an invariant measure with a non-negative normal Lyapunov exponent.Mathematics, AppliedMathematicsSCI(E)0ARTICLE3409-4171
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The Birkhoff Ergodic Theorem asserts under mild conditions that Birkhoff averages (i.e. time average...
Abstract. We prove almost sure ergodic theorems for a class of systems called qua-sistatic dynamical...
AbstractWe prove a conditioned version of the ergodic theorem for Markov processes, which we call a ...
Let a(x) be a real function with a regular growth as x → (∞). [The precise technical assumption is t...
We prove the existence and uniqueness of quasi-stationary and quasi-ergodic measures for a class of ...
AbstractRecently, Bass and Pyke proved a strong law of large numbers for d-dimensional arrays of i.i...
It is well-known that a strict analogue of the Birkhoff Ergodic Theorem in infinite ergodic theory i...
We consider a class of ordinary differential equations describing one-dimensional analytic systems ...
International audienceWe prove a version of Furstenberg's ergodic theorem with restrictions on retur...
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summary:The author investigates non ergodic versions of several well known limit theorems for strict...
We prove a conditioned version of the ergodic theorem for Markov processes, which we call a quasi-er...
We consider non-conservative positive semigroups and obtain necessary and sufficient conditions for ...
We establish the existence and fundamental properties of the equilibrium measure in uniformly quasi...
We provide an elementary proof that ergodic measures on one-sided shift spaces are ‘uniformly scalin...