Integer Cantor sets and an order-two ergodic theorem
نویسندگان
چکیده
منابع مشابه
Two measures on Cantor sets
We give an example of Cantor-type set for which its equilibrium measure and the corresponding Hausdorff measure are mutually absolutely continuous. Also we show that these two measures are regular in the Stahl–Totik sense. c ⃝ 2014 Elsevier Inc. All rights reserved. MSC: 30C85; 31A15; 28A78; 28A80
متن کاملOn Arithmetical Difference of Two Cantor Sets
We construct a large class of dynamically defined Cantor sets on the real line whose self-difference sets are Cantor sets of arbitrary positive measure. This relates to a question posed by J. Palis which arises naturally in the context of homoclinic bifurcations in dimension 2. §
متن کاملCantor sets
This paper deals with questions of how many compact subsets of certain kinds it takes to cover the space ω of irrationals, or certain of its subspaces. In particular, given f ∈ (ω\{0}), we consider compact sets of the form Q i∈ω Bi, where |Bi| = f(i) for all, or for infinitely many, i. We also consider “n-splitting” compact sets, i.e., compact sets K such that for any f ∈ K and i ∈ ω, |{g(i) : ...
متن کاملAn Ergodic Adding Machine on the Cantor Set
We calculate all ergodic measures for a specific function F on the unit interval. The supports of these measures consist of periodic orbits of period 2n and the classical ternary Cantor set. On the Cantor set, F is topologically conjugate to an “adding machine” in base 2. We show that F is representative of the class of functions with zero topological entropy on the unit interval, already analy...
متن کاملErgodic theorem, ergodic theory, and statistical mechanics.
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundam...
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: Ergodic Theory and Dynamical Systems
سال: 1993
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385700007197