He operates at the crossroads where number theory/uniform distribution intersects dynamical systems/quantitative ergodic theory
, he says; it is pure mathematics with rigorous proofs, though he borrows some motivation and intuitions from physics and uses some probability theory.
Rocha, Contributions to the geometric and ergodic theory
of conservative flows, Ergodic Theory
We propose to combine these new geometrical ideas to the ergodic theory
of non-uniformly hyperbolic systems.
Can we construct a special master-space by the fusion of manifold concepts , soft topology , Ergodic theory
,with Neutrosophic distribution ?
Characteristic Lyapunov exponents and smooth ergodic theory
," Russian Math.
Over the years and under different names statistical convergence has been discussed in the theory of Fourier analysis, Ergodic theory
, Number theory, Measure theory, Trigonometric series, Turnpike theory and Banach spaces.
Among the topics are the ergodic theory
of hyperbolic groups, harmonic maps and integrable systems, left-orderability and exceptional Dehn surgery on two-bridge knots, the commensurability of knots and L2-unvariants, the number of hyperbolic 3-manifolds of a given volume, and 3-manifolds with Heegaard splittings of distance two.
He is a mathematician, specialising in ergodic theory
The presence of natural invariant measures allows one to study CA as measure-preserving dynamical systems, applying results from ergodic theory
In addition, it is mentioned that some authors, basing their ideas on the exchangeability property, on the principles of the representation theorem and on its interpretation in the ambit of ergodic theory
, which allows to show that the probability distribution of a stochastic process in certain conditions, can be defined in terms of averages in the time domain, raised the possibility of the existence of objective probabilities that have a physical meaning and therefore are not liable to subjective interpretation.
In spite of the unpredictability of chaotic systems, the so called ergodic theory
proves that, under rather general additional hypothesis, there exists a decomposition of the space into abstract invariant-measure structures, called ergodic measures (Mane, 1987).
Crauel, "Iterated function systems and multiplicative ergodic theory
," en Diffusion Processes and Related Problems in Analysis, Vol.