Results 51 to 60 of about 243 (89)
Bounds for the 3x+1 Problem using Difference Inequalities
, 2002 We study difference inequality systems for the 3x+1 problem introduced by the first author in 1989. These systemes can be used to give lower bounds for the number of integers below x that contain 1 in their forward orbit under the 3x+1 map.
Krasikov, Ilia, Lagarias, Jeffrey C.
core +2 more sources
Hausdorff Dimensions of Self-Similar and Self-Affine Fractals in the Heisenberg Group [PDF]
, 2017 We study the Hausdorff dimensions of invariant sets for self-similar and self-affine iterated function systems in the Heisenberg group. In our principal result we obtain almost sure formulae for the dimensions of self-affine invariant sets, extending to ...
Balogh, Zoltán M., Tyson, Jeremy T.
core
On Functions with Monotonic Differences
Annales Mathematicae SilesianaeMotivated by the Szostok problem on functions with monotonic differences (2005, 2007), we consider a-Wright convex functions as a generalization of Wright convex functions.
Rajba Teresa
doaj +1 more source
$3x+1$ inverse orbit generating functions almost always have natural boundaries [PDF]
, 2014 The $3x+k$ function $T_{k}(n)$ sends $n$ to $(3n+k)/2$ resp. $n/2,$ according as $n$ is odd, resp. even, where $k \equiv \pm 1~(\bmod \, 6)$. The map $T_k(\cdot)$ sends integers to integers, and for $m \ge 1$ let $n \rightarrow m$ mean that $m$ is in the
C. Lagarias, Jason P. Bell, Jeffrey
core
Turbulent maps and their ω-limit sets
, 1997 One-dimensional turbulent maps can be characterized via their ω-limit sets [1]. We give a direct proof of this characterization and get stronger results, which allows us to obtain some other results on ω-limit sets, which previously were difficult to ...
F. Balibrea, C. L. Paz
semanticscholar +1 more source
Descending Dungeons and Iterated Base-Changing
, 2006 For real numbers a, b> 1, let as a_b denote the result of interpreting a in base b instead of base 10. We define ``dungeons'' (as opposed to ``towers'') to be numbers of the form a_b_c_d_..._e, parenthesized either from the bottom upwards (preferred) or ...
Marc Lebrun +5 more
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On barycentric subdivision, with simulations [PDF]
, 2010 Consider the barycentric subdivision which cuts a given triangle along its medians to produce six new triangles. Uniformly choosing one of them and iterating this procedure gives rise to a Markov chain.
Diaconis, Persi, Miclo, Laurent
core +2 more sources
Some properties of a function studied by De Rham, Carlitz and Dijkstra and its relation to the (Eisenstein-)Stern\u27s diatomic sequence [PDF]
, 2001 We present a novel approach to a remarkable function D: N_0→N_0 defined by D(0)=0, D(1)=1, D(2n)=D(n), D(2n+1)=D(n)+D(n+1), studied independently by well known researchers in different areas of mathematics and computer science.
I. Urbiha
core
Unfolding chaotic quadratic maps --- parameter dependence of natural measures
, 1998 We consider perturbations of quadratic maps $f_a$ admitting an absolutely continuous invariant probability measure, where $a$ is in a certain positive measure set $\mathcal{A}$ of parameters, and show that in any neighborhood of any such an $f_a$, we ...
Thunberg, Hans
core +2 more sources
Fixed points and iterations of mean-type mappings
Open Mathematics, 2012 Matkowski Janusz
doaj +1 more source