The significant cylindrical condition and a Hausdorff rectifiable set
نویسندگان
چکیده
منابع مشابه
Historic set carries full hausdorff dimension
We prove that the historic set for ratio of Birkhoff average is either empty or full of Hausdorff dimension in a class of one dimensional non-uniformly hyperbolic dynamical systems.
متن کاملH$^*$-condition on the set of submodules of a module
In this work, we introduce $H^*$-condition on the set of submodules of a module. Let $M$ be a module. We say $M$ satisfies $H^*$ provided that for every submodule $N$ of $M$, there is a direct summand$D$ of $M$ such that $(N+D)/N$ and $(N+D)/D$ are cosingular. We show that over a right perfect right $GV$-ring,a homomorphic image of a $H^*$ duo module satisfies $H^*$.
متن کاملEquivalence of Positive Hausdorff Measure and the Open Set Condition for Self-conformal Sets
A compact set K is self-conformal if it is a finite union of its images by conformal contractions. It is well known that if the conformal contractions satisfy the “open set condition” (OSC), then K has positive sdimensional Hausdorff measure, where s is the solution of Bowen’s pressure equation. We prove that the OSC, the strong OSC, and positivity of the s-dimensional Hausdorff measure are equ...
متن کاملHausdorff Measures and Two Point Set Extensions
We investigate the question: under which conditions is a-compact partial two point contained in a two point set? We show that no reasonable measure or capacity (when applied to the set itself) can provide a suucient condition for a compact partial two point set to be extendable to a two point set. On the other hand, we prove that under Martin's Axiom any-compact partial two point set such that ...
متن کاملThe Newhouse Set Has a Positive Hausdorff Dimension
The Newhouse phenomenon of infinitely many coexisting periodic attractors is studied in its simplest form. One shows that the corresponding parameter set (the Newhouse set) JN has a strictly positive Hausdorff dimension. This result is stronger than that of Tedeschini-Lalli and Yorke [Commun. Math. Phys. 106, 635 (1986)] concerning the Lebesgue measure of the Newhouse set; and is complementary ...
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: Proceedings of the American Mathematical Society
سال: 1973
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1973-0311876-4