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 ...

The Euclidean group (Rn,+) where (n?N, plays a key role in harmonic analysis. If we consider the Lebesgue measure ()nd?xR as the Haar measure of this group then 12(2)()nd?x=d?RR. In this article we look for LCA groups K, whose Haar measures have a similar property. In fact we will show that for some LCA groups K with the Haar measure K?, there exists a constant such that 0KC>()(2)KKK?A=C?A for ...

We investigate graph-directed iterated function systems in mixed Euclidean and p-adic spaces. Hausdorff measure and Hausdorff dimension in such spaces are defined, and an upper bound for the Hausdorff dimension is obtained. The relation between the Haar measure and the Hausdorff measure is clarified. Finally, we discus an example in R×Q2 and calculate upper and lower bounds for its Hausdorff di...

Throughout this note we will use the following standard notation from elementary number theory: p denotes a prime number, μ(n) is the Möbius function, φ(n) is the Euler phi function, ω(n) denotes the number of distinct prime divisors of n, and τ(n) is the number of positive integers which divide n. Also we use λ to denote Lebesgue measure on R/Z and dimX to denote the Hausdorff dimension of a s...

For a sequence (cn) of complex numbers we consider the quadratic polynomials fcn(z) := z 2 + cn and the sequence (Fn) of iterates Fn := fcn ◦ · · · ◦ fc1 . The Fatou set F(cn) is by definition the set of all z ∈ Ĉ such that (Fn) is normal in some neighbourhood of z, while the complement of F(cn) is called the Julia set J(cn). The aim of this article is to study geometric properties, Lebesgue me...

In this paper, we propose a new similarity measure to combine multiple views of 3-D objects for non-rigid registration. It is a metric that integrates multiple 2-D view features representing a visual identity of a 3-D object seen from different viewpoints. The robustness to non-rigid distortions is achieved by the proximity correspondence manner. The human face, a typical non-rigid object, was ...

Let T be a positive plurisubharmonic current of bidimension (p, p) and δ > 0. Assume that the Lelong number of T satisfies ν(T, a) ≥ δ on a dense subset of supp(T) (rectifiable currents satisfy this condition). Then T = ϕ[X], where X is a complex subvariety of pure dimension p and ϕ is a weakly plurisubharmonic function on X. We also show that if T is positive pluriharmonic and its support has ...

g. darbo [rend. sem. math. univ. padova, 24 (1955) 84--92] used the measure of noncompactness to investigate operators whose properties can be characterized as being intermediate between those of contraction and compact operators. in this paper, we apply the darbo's fixed point theorem for solving infinite system of linear equations in some sequence spaces.

We study parabolic iterated function systems with overlaps on the real line. We show that if a d-parameter family of such systems satisfies a transversality condition, then for almost every parameter value the Hausdorff dimension of the limit set is the minimum of 1 and the least zero of the pressure function. Moreover, the local dimension of the exceptional set of parameters is estimated. If t...

It is a classical result that a closed exceptional polar set is removable for subharmonic functions which are bounded above. Gardiner has shown that in the case of a compact exceptional set the above boundedness condition can be relaxed by imposing certain smoothness and Hausdorff measure conditions on the set. We give related results for a closed exceptional set, by replacing the smoothness an...