| We have a long way to go before we understand the ergodic theory of strange attractors. |
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| While in the Harvard College Observatory he worked on many mathematical and astronomical subjects including topology and ergodic theory. |
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| Here, there are various results demonstrating that strongly ergodic classical billiards, when quantized, exhibit quantum ergodicity. |
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| Doeblin also contributed to the theory of random chains with complete connection, some of which was used in a paper by him on ergodic properties of continued fractions. |
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| Under appropriate assumptions on the boundary conditions and on the services, we obtain ergodic results for both versions of the model. |
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| This duality structure, interesting by itsetf, is also instrumental in proving some of the ergodic results. |
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| In the more difficult half plane problem, the aim is to obtain evolutions which are both temporally and spatially ergodic. |
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| In the stochastic case, we prove a multiplicative ergodic theorem, asserting that the stochastic spectral vector exists in all cases. |
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| For the quadrant version, we prove the existence of temporally ergodic evolutions and of spatially ergodic ones. |
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| Armed with this understanding of the definition of ergodicity, we can now discuss some important properties of ergodic systems. |
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| He introduced ergodic methods into number theory in his first work. |
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| His ergodic theorem gave the kinetic theory of gases a rigorous basis. |
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| Berkowitz et al. 2006 argue that in fact an epistemic conception of randomness as unpredictability is the only way to understand the ergodic hierarchy of ergodicity, mixing, and Bernoulli properties of systems. |
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| And those who advocate Boltzmann while rejecting ergodic theory, may similarly be reminded that the latter theory too originated with Boltzmann himself. |
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| All other ergodic invariant Radon measures are squashable, and there are infinitely many such measures. |
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| The proposed research is an investigation of intermediate chaos in ergodic theory of dynamical systems. |
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| His thesis examines the paratextual and ergodic elements of Douglas Coupland's novels. |
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| Terms such as ergodic effort and diegetic information, among others, are discussed. |
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| This choice of terminology is somewhat misleading, since ergodicity is only the bottom level of this hierarchy and so EH contains much more than ergodicity and the scope of ergodic theory stretches far beyond ergodicty. |
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| The object of study in ergodic theory is a dynamical system. |
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| He made notable contributions in many other areas, including ergodic theory, orthonormal series, the theory of partially ordered vector spaces, and topology. |
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| They pointed out that the microscopic ergodic theories of John von Neumann and Eberhard Hopf are not relevant to the problem of ergodic behavior in molecules. |
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| In an ergodic forest, while the size, shape and spacing of individual trees may vary, their distribution in any given area is the same as any other area. |
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| This list could be expanded to include most fields of mathematics, including measure theory, ergodic theory, probability, representation theory, and differential geometry. |
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| If the process is spatially ergodic, then the histogram of the realized noise can be expected to resemble the distribution of the noise process itself. |
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| Three surveys discuss ultraproducts of first order structures, set-theoretic aspects of ultrafilters, and connections with ergodic theory and combinatorics. |
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| Over the years and under different names statistical convergence has been discussed in the theory of Fourier analysis, ergodic theory and number theory. |
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