1,721,031 research outputs found
Maps Conjugating Holomorphic Maps in Cn
No full textAbstract. If is a bijection from Cn onto a complex manifold M, which conjugates every holomorphic map in Cn to an endomorphism in M, then we prove that is necessarily biholomorphic or antibiholomorphic. This extends a result of A. Hinkkanen to higher dimensions. As a corollary, we prove that if there is an epimorphism from the semigroup of all holomorphic endomorphisms of Cn to the semigroup of holomorphic endomorphisms in M, or an epimor-phism in the opposite direction for a doubly-transitive M, then it is given by conjugation by some biholomorphic or antibiholomorphic map. We show also that there are two unbounded domains in Cn with isomorphic endomorphism semigroups but which are neither biholomorphically nor antibiholomorphically equivalent. 1
Holomorphic motions and structural stability for polynomial automorphisms of C2
No full textAbstract. Combining ideas from real dynamics on compact manifolds and complex dy-namics in one variable, we prove the structural stability of hyperbolic polynomial automor-phisms in C2. We consider families of hyperbolic polynomial automorphisms depending holomorphically on the parameter . This is done over a series of steps- given a family ffg, where jj is suciently small, we construct mappings dened on a neighborhood U of J0 which conjugate f0 and f. Moreover, it is shown that J moves holomorphically. This conjugacy is then used to construct a conjugacy between f0 and f dened on a neighborhood M of J+0 [J−0. Finally, we extend such a mapping to construct a conjugacy on all of C2. 1
Variance-Based Global Sensitivity Analysis via Sparse-Grid Interpolation and Cubature
No full textAbstractThe stochastic collocation method using sparse grids has become a popular choice for performing stochastic computations in high dimensional (random) parameter space. In addition to providing highly accurate stochastic solutions, the sparse grid collocation results naturally contain sensitivity information with respect to the input random parameters. In this paper, we use the sparse grid interpolation and cubature methods of Smolyak together with combinatorial analysis to give a computationally efficient method for computing the global sensitivity values of Sobol’. This method allows for approximation of all main effect and total effect values from evaluation of f on a single set of sparse grids. We discuss convergence of this method, apply it to several test cases and compare to existing methods. As a result which may be of independent interest, we recover an explicit formula for evaluating a Lagrange basis interpolating polynomial associated with the Chebyshev extrema. This allows one to manipulate the sparse grid collocation results in a highly efficient manner.</jats:p
Tame sets, dominating maps, and complex tori
No full textAbstract. A discrete subset of Cn is said to be tame if there is an automor-phism of Cn taking the given discrete subset to a subset of a complex line; such tame sets are known to allow interpolation by automorphisms. We give here a fairly general sufficient condition for a discrete set to be tame. In a related direction, we show that for certain discrete sets in Cn there is an injective holo-morphic map from Cn into itself whose image avoids an -neighborhood of the discrete set. Among other things, this is used to show that, given any complex n-torus and any finite set in this torus, there exist an open set containing the finite set and a locally biholomorphic map from Cn into the complement of this open set. 1
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