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1.
Suppose f(z) is a quadratic rational map with two Siegel disks. If the rotation numbers of the Siegel disks are both of bounded type, the Hausdorff dimension of the Julia set satisfies Dim (J(f))〈2. 相似文献
2.
3.
Let be a quadratic rational map of the sphere which has two fixed Siegel disks with bounded type rotation numbers and . Using a new degree Blaschke product model for the dynamics of and an adaptation of complex a priori bounds for renormalization of critical circle maps, we prove that can be realized as the mating of two Siegel quadratic polynomials with the corresponding rotation numbers and .
4.
We study quasiconformal Siegel disks with critical points in their boundaries. The main result asserts that every subarc of
the boundary of the Siegel disk has the Hausdorff dimension strictly larger than 1 and that the boundary does not have a tangent
at any point.
Oblatum 19-V-2000 & 4-X-2001?Published online: 18 January 2002 相似文献
5.
Arnaud Chéritat 《Mathematische Annalen》2011,349(3):529-542
We construct holomorphic maps f with a Siegel disk whose boundary is not locally connected (and is an indecomposable continuum), yet compactly contained
in the domain of definition of the map. Our examples are injective and defined on a subset of
\mathbb C{\mathbb C}. 相似文献
6.
《Journal of Pure and Applied Algebra》2023,227(3):107215
If a K3 surface admits an automorphism with a Siegel disk, then its Picard number is an even integer between 0 and 18. Conversely, using the method of hypergeometric groups, we are able to construct K3 surface automorphisms with Siegel disks that realize all possible Picard numbers. The constructions involve extensive computer searches for appropriate Salem numbers and computations of algebraic numbers arising from holomorphic Lefschetz-type fixed point formulas and related Grothendieck residues. 相似文献
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8.
Gaofei Zhang 《Inventiones Mathematicae》2011,185(2):421-466
We prove that every bounded type Siegel disk of a rational map must be a quasi-disk with at least one critical point on its
boundary. This verifies Douady-Sullivan’s conjecture in the case of bounded type rotation numbers. 相似文献
9.
We describe a new convex quadratic programming bound for the quadratic assignment problem (QAP). The construction of the bound
uses a semidefinite programming representation of a basic eigenvalue bound for QAP. The new bound dominates the well-known
projected eigenvalue bound, and appears to be competitive with existing bounds in the trade-off between bound quality and
computational effort.
Received: February 2000 / Accepted: November 2000?Published online January 17, 2001 相似文献
10.
Terry A. McKee 《Order》1989,6(3):265-275
The study of upper bound graphs of posets can be extended naturally to multigraphs. This paper characterizes such upper bound multigraphs, shows they determine the associated posets up to isomorphism, and extends results of D. Scott to characterize posets having chordal or interval upper bound multigraphs.Research partially supported by Office of Naval Research contract N00014-88-K-0163. 相似文献
11.
Summary We present an algorithm which combines standard active set strategies with the gradient projection method for the solution of quadratic programming problems subject to bounds. We show, in particular, that if the quadratic is bounded below on the feasible set then termination occurs at a stationary point in a finite number of iterations. Moreover, if all stationary points are nondegenerate, termination occurs at a local minimizer. A numerical comparison of the algorithm based on the gradient projection algorithm with a standard active set strategy shows that on mildly degenerate problems the gradient projection algorithm requires considerable less iterations and time than the active set strategy. On nondegenerate problems the number of iterations typically decreases by at least a factor of 10. For strongly degenerate problems, the performance of the gradient projection algorithm deteriorates, but it still performs better than the active set method.Work supported in part by the Applied Mathematical Sciences subprogram of the Office of Energy Research of the U.S. Department of Energy under Contract W-31-109-Eng-38 相似文献
12.
Approximating quadratic programming with bound and quadratic constraints 总被引:27,自引:3,他引:24
Yinyu Ye 《Mathematical Programming》1999,84(2):219-226
Received May 20, 1997 / Revised version received March 9, 1998 Published online October 9, 1998 相似文献
13.
This paper is concerned with the blow-up solutions of Gross-Pitaevskii equation. We obtain the upper bound of weak-limitation for the blow-up solutions by using the method of Cazenave (2003) [3] as well as the concentration compact principle. 相似文献
14.
15.
Isabella Novik 《Israel Journal of Mathematics》1998,108(1):45-82
In this paper we prove the Upper Bound Conjecture (UBC) for some classes of (simplicial) homology manifolds: we show that
the UBC holds for all odd-dimensional homology manifolds and for all 2k-dimensional homology manifolds Δ such that β
k
(Δ)⩽Σ{β
i
(Δ):i ≠k-2,k,k+2 and 1 ⩽i⩽2k-1}, where β
i
(Δ) are reduced Betti numbers of Δ. (This condition is satisfied by 2k-dimensional homology manifolds with Euler characteristic χ≤2 whenk is even or χ≥2 whenk is odd, and for those having vanishing middle homology.)
We prove an analog of the UBC for all other even-dimensional homology manifolds.
Kuhnel conjectured that for every 2k-dimensional combinatorial manifold withn vertices,
. We prove this conjecture for all 2k-dimensional homology manifolds withn vertices, wheren≥4k+3 orn≤3k+3. We also obtain upper bounds on the (weighted) sum of the Betti numbers of odd-dimensional homology manifolds. 相似文献
16.
Let U be an open subset of the Riemann sphere \(\hat {\mathbb{C}}\). We give sufficient conditions for which a finite type map f: U → \(\hat {\mathbb{C}}\) with at most three singular values has a Siegel disk compactly contained in U and whose boundary is a quasicircle containing a unique critical point. The main tool is quasiconformal surgery à la Douady-Ghys-Herman-?wi?tek. We also give sufficient conditions for which, instead, Δ has not compact closure in U. The main tool is the Schwarzian derivative and area inequalities à la Graczyk-?wi?tek. 相似文献
17.
Yong Xia 《Frontiers of Mathematics in China》2008,3(1):109-118
The Gilmore-Lawler bound (GLB) is one of the well-known lower bound of quadratic assignment problem (QAP). Checking whether
GLB is tight is an NP-complete problem. In this article, based on Xia and Yuan linearization technique, we provide an upper
bound of the complexity of this problem, which makes it pseudo-polynomial solvable. We also pseudopolynomially solve a class
of QAP whose GLB is equal to the optimal objective function value, which was shown to remain NP-hard.
相似文献
18.
We prove 2 7/9v for 3-partite hypergraphs. (This is an improvement of the trivial bound 3v.) 相似文献
19.
A. Pohl 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2007,77(1):129-136
Using matrix representation of continued fractions we give an upper bound for the period length of a quadratic irrational which improves the result byPodsypanin. 相似文献