Analysis of invariant measures in dynamical systems by Hausdorff measure
نویسندگان
چکیده
منابع مشابه
Measure Theory on Hausdorff Measures
Let y = h(x) be defined for 0 < x < oo and assume values in 0 ^ y ^ + co. Let S be any linear set of points and p an arbitrary positive number. Cover S by a countable number of open intervals h , I2, • • • of lengths xx, x2 , • • • each of which is less than p, and denote by mp(S; h) the lower bound of h(xi) + h(x2) + • • • for all such coverings of S. Then m(S; h) = limp|0mp(/S; h) is called t...
متن کاملOn the computation of invariant measures in random dynamical systems
Invariant measures of dynamical systems generated e. g. by difference equations can be computed by discretizing the originally continuum state space, and replacing the action of the generator by the transition mechanism of a Markov chain. In fact they are approximated by stationary vectors of these Markov chains. Here we extend this well known approximation result and the underlying algorithm t...
متن کاملCoherent Upper Conditional Previsions Defined by Hausdorff Outer Measures to Forecast in Chaotic Dynamical Systems
Coherent conditional previsions and probabilities are tools to model and quantify uncertainties; they have been investigated in de Finetti [3], [4], Dubins [10] Regazzini [13], [14] and Williams [20]. Separately coherent upper and lower conditional previsions have been introduced in Walley [18], [19] and models of upper and lower conditional previsions have been analysed in Vicig et al. [17] an...
متن کاملNumerical Modeling of Toroidal Dynamical Systems with Invariant Lebesgue Measure
Computer simulat ions of dynamical systems can cont ain bot h discretizations, in which finite machine arithmet ic replaces cont inuum state spaces , and realizations , in which a continuous syste m is replaced by some approximation such as a computational method. In some circumstances, complicated theoret ical behavior collapses to t rivial and degenerate behavior. In others, the computation m...
متن کاملApproximating Physical Invariant Measures of Mixing Dynamical Systems
Invariant measures of higher dimensional transformations are hard to calculate. We present new results on the estimation of absolutely continous invariant measures of mixing transformations , including a new method of proof of Ulam's conjecture. The method involves constructing nite matrix approximations to the Perron-Frobenius operator from increasingly ner partitions of the state space X. We ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1987
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1987.129.385