Download Continua: With the Houston Problem Book by Howard Cook, William T. Ingram, Krystyna Kuperberg, Andrew PDF

By Howard Cook, William T. Ingram, Krystyna Kuperberg, Andrew Lelek, Piotr Minc

This quantity includes the complaints of the exact consultation on sleek tools in Continuum thought awarded on the a hundredth Annual Joint arithmetic conferences held in Cincinnati, Ohio. It additionally gains the Houston challenge e-book which incorporates a lately up to date set of 2 hundred difficulties amassed over a number of years on the college of Houston.;These court cases and difficulties are aimed toward natural and utilized mathematicians, topologists, geometers, physicists and graduate-level scholars in those disciplines.

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Extra info for Continua: With the Houston Problem Book

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The following theorem appears in [1]. We assume that the eigenvalues of D f evaluated at each saddle of the accessible twist pair are positive. T heorem 3. Let f be an area-contracting diffeomorphism into the annulus^ iso­ topic to the identity. Assume pi and pe are rational with pi < pe^ and assume the hypotheses of Theorem IB on 0 and on both internal and external accessible peri­ odic orbits. If there exists an accessible twist pair for 0, then, for each a € [piy Pe]i there is a point x in Q such that p{x) = a.

The following theorem is proved in [3]: Theorem 2 . Let f be an orientation-preserving diffeomorphism of the plane or annulus. Assume thatp and q form a heteroclinic pair with p{p) = a/b^ and p{q) = c/d, {c/d > a/b). Then for each a, a G [a/6, c/d], there is a point in D with rotation number a. 21 ROTATION SETS FOR INVARIANT CONTINUA Remark Specifically, for each a, a € [a/ 6, c/ci], there is a continuum F in D (ex­ tending from L to R) such that p~^{x) = a for each x G F. Similarly, there is a continuum A in D (extending from B to T) such that p~{y) = oi for each y G A.

The first named author was partially supported by NSERC grant No. OGP0155552 ** the second named author was supported by an NSERC International Fellowship *** the third named author was partially supported by NSERC grant No. A5616 The paper was written while the second author was visiting the University of Saskatchewan. 37 38 CHIGOGIDZE, KAWAMURA AND TYMGHATYN 3. 1. 2. 3. Group actions on Menger manifolds, connections with the Hilbert-Smith conjecture 4. 1. 2. HausdorfF dimension 5. 1. 2. Pseudo-boundaries and pseudo-interiors of Euclidean spaces and Menger compacta 6.

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