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作者：Boyle, M; Downarowicz, T
作者单位：University System of Maryland; University of Maryland College Park; Wroclaw University of Science & Technology
摘要：Fix a topological system (X, T), with its space K(X, T) of T-Invariant Borel probabilities. If (Y, S) is a symbolic system (subshift) and phi : (Y, S) (X, T) is a topological extension (factor map), then the function h(ext)(phi) on K(X, T) which assigns to each mu the maximal entropy of a measure nu on Y mapping to mu is called the extension entropy function of phi. The infimum of such functions over all symbolic extensions is called the symbolic extension entropy function and is denoted by h(...
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作者：Kostant, B
作者单位：Massachusetts Institute of Technology (MIT)
摘要：If g is a complex simple Lie algebra, and k does not exceed the dual Coxeter number of g, then the absolute value of the k(th) coefficient of the dim g power of the Euler product may be given by the dimension of a subspace of boolean AND(k) g defined by all abelian subalgebras of g of dimension k. This has implications for all the coefficients of all the powers of the Euler product. Involved in the main results are Dale Peterson's 2(rank) theorem on the number of abelian ideals in a Borel suba...
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作者：Buff, X; Chéritat, A
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：If alpha is an irrational number, we let {p(n)/q(n)}(ngreater than or equal to0), be the approximants given by its continued fraction expansion. The Bruno series B(alpha) is defined as [GRAPHICS] The quadratic polynomial P-alpha : z \--> l(2ipipialpha) z + z(2) has an indifferent fixed point at the origin. If P-alpha is linearizable, we let r(alpha) be the conformal radius of the Siegel disk and we set r(alpha) = 0 otherwise. Yoccoz proved that if B(alpha) = infinity, then r(alpha) = 0 and P-a...
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作者：Khare, C; Ramakrishna, R
作者单位：Tata Institute of Fundamental Research (TIFR); Utah System of Higher Education; University of Utah; Cornell University
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作者：Przytycki, F; Rivera-Letelier, J; Smirnov, S
作者单位：Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; State University of New York (SUNY) System; Stony Brook University; Royal Institute of Technology
摘要：We show equivalence of several standard conditions for non-uniform hyperbolicity of complex rational functions, including the Topological Collet-Eckmann condition (TCE), Uniform Hyperbolicity on Periodic orbits, Exponential Shrinking of components of pre-images of small discs, backward Collet-Eckmann condition at one point, positivity of the infimum of Lyapunov exponents of finite invariant measures on the Julia set. The condition TCE is stated in purely topological terms, so we conclude that ...
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作者：Mendelson, S; Vershynin, R
作者单位：Australian National University; University of Alberta
摘要：We solve Talagrand's entropy problem: the L-2-covering numbers of every uniformly bounded class of functions are exponential in its shattering dimension. This extends Dudley's theorem on classes of {0, 1}-valued functions, for which the shattering dimension is the Vapnik-Chervonenkis dimension. In convex geometry, the solution means that the entropy of a convex body K is controlled by the maximal dimension of a cube of a fixed side contained in the coordinate projections of K. This has a numbe...
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作者：Nakamura, G; Uhlmann, G
作者单位：Hokkaido University; University of Washington; University of Washington Seattle
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作者：Ghrist, RW; Van den Berg, JB; Vandervorst, RC
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; University of Nottingham; Vrije Universiteit Amsterdam; University System of Georgia; Georgia Institute of Technology
摘要：In the first half of the paper we construct a Morse-type theory on certain spaces of braid diagrams. We define a topological invariant of closed positive braids which is correlated with the existence of invariant sets of parabolic flows defined on discretized braid spaces. Parabolic flows, a type of one-dimensional lattice dynamics, evolve singular braid diagrams in such a way as to decrease their topological complexity; algebraic lengths decrease monotonically. This topological invariant is d...
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作者：Premet, A
作者单位：University of Manchester
摘要：Let G be a connected reductive algebraic group over an algebraically closed field k of characteristic p greater than or equal to 0, and g = Lie G. In positive characteristic, suppose in addition that p is good for G and the derived subgroup of G is simply connected. Let N = N(g) denote the nilpotent variety of g, and C-nil(g) := {(x,y) is an element of N x N \ [x, y] = 0}, the nilpotent commuting variety of g. Our main goal in this paper is to show that the variety C-nil(g) is equidimensional....
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作者：Karpenko, NA
作者单位：Universite de Lille
摘要：We prove Hoffmann's conjecture determining the possible values of the first Witt index of anisotropic quadratic forms of any given dimension. The proof makes use of the Steenrod type operations on the modulo 2 Chow groups constructed by P. Brosnan.
