相关论文: There are no C^1-stable intersections of regular C…
In the present paper, We introduce a pair of middle Cantor sets namely $(C_\alpha, C_\beta)$ having stable intersection, while the product of their thickness is smaller than one. Furthermore, the arithmetic difference $C_\alpha- \lambda…
In this paper, we construct (a) a pair of two regular Cantor sets in higher dimension which exhibits $C^1$-stable intersection and (b) a hyperbolic basic set which exhibits $C^2$-robust homoclinic tangency of the largest codimension for any…
Let $\{f_\mu\}_{\mu \in \mathbb{D}}$ be a family of automorphisms of $\mathbb{C}^2$ unfolding a generic homoclinic tangency associated to a fixed point $p$ belonging to a horseshoe. We prove that if the linearized versions of the Cantor…
It is proved that -- consistently -- there can be no ccc closed P-sets in the remainder space omega^* .
We prove that a distance-regular graph with intersection array {56,36,9;1,3,48} does not exist. This intersection array is from the table of feasible parameters for distance-regular graphs in "Distance-regular graphs"\ by A.E. Brouwer, A.M.…
We prove that a distance-regular graph with intersection array $\{55,36,11;1,4,45\}$ does not exist. This intersection array is from the table of feasible parameters for distance-regular graphs in "Distance-regular graphs"\ by A.E. Brouwer,…
We investigate stable intersections of conformal Cantor sets and their consequences to dynamical systems. First we define this type of Cantor set and relate it to horseshoes appearing in automorphisms of $\C^2$. Then we study limit…
We construct several models where there are no strongly meager sets of size continuum. In particular, there are no such sets in the Laver's model.
We prove that a structurally stable diffeomorphism of a closed (2m+1)-manifold has no codimension one non-orientable expanding attractors.
We prove a necessary and sufficient condition for a $ C^1 $-hypersurface to have all parallel sets nowhere $ C^1 $-regular. As a corollary, we deduce that for a generic $ C^1 $-regular convex body all interior parallel bodies have nowhere $…
We show that there are no nontrivial solutions of the Seiberg-Witten equations on R^8 with constant standard spin^c structure.
It is well known that a pair of compact sets in $\mathbb{R}^d$ ($d \in \mathbb{N}$) can be separated by small deformations if the sum of their upper box dimensions is less than $d$. In this paper, we demonstrate that this dimension…
We prove that there do not exist multisoliton solutions of noncommutative scalar field theory in the Moyal plane which interpolate smoothly between $n$ overlapping solitons and $n$ solitons with an infinite separation.
Cantor sets are constructed from iteratively removing sections of intervals. This process yields a cumulative distribution function (CDF), constructed from the invariant measure associated with their iterated function systems. Under…
We obtain some results about continuum-wise expansive homeomorphisms, such as non-existence of stable points and presence of non-trivial connected components within the local stable and unstable sets. These facts have been of importance in…
We obtain some nonexistence results for complete noncompact stable hyppersurfaces with nonnegative constant scalar curvature in Euclidean spaces. As a special case we prove that there is no complete noncompact strongly stable hypersurface…
We prove that Rado's graph admits no quantum symmetries.
Cantor's famous proof of the non-denumerability of real numbers does apply to any infinite set. The set of exclusively all natural numbers does not exist. This shows that the concept of countability is not well defined. There remains no…
A generalization of a result of Wermer concerning the existence of polynomial hulls without analytic discs is presented. As a consequence it is shown that there exists a Cantor set $X$ in ${\mathbb C}^3$ whose polynomial hull is strictly…
Let C be a Cantor set. For a real number t let C+t be the translate of C by t, We say two real numbers s,t are equivalent if the intersection of C and C+s is a translate of the intersection of C and C+t. We consider a class of Cantor sets…