By Howard Cook, William T. Ingram, Krystyna Kuperberg, Andrew Lelek, Piotr Minc
This quantity comprises the court cases of the specified consultation on sleek tools in Continuum idea offered on the a hundredth Annual Joint arithmetic conferences held in Cincinnati, Ohio. It additionally positive factors the Houston challenge e-book which incorporates a lately up to date set of 2 hundred difficulties gathered over a number of years on the collage of Houston.;These complaints and difficulties are aimed toward natural and utilized mathematicians, topologists, geometers, physicists and graduate-level scholars in those disciplines.
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Extra resources for Continua: With the Houston Problem Book
Example text
Theory of Cluster Sets. Cambridge Tracts in Mathematics and Mathematical Physics, No. 56, Cambridge Univer sity Press, Cambridge. 11 . R. Devaney. 1986. An Introduction to Chaotic Dynamical Systems, Benjamin/Cummings, Menlo Park, CA. 12. M. Handel, The rotation set of a homeomorphism of the annulus is closed. Commun. Math. Phys. 127, 339-349. 13. K. Hockett and P. Holmes, Josephson’s junction, annulus maps, Birkhoff attrac tors, horseshoes and rotation sets, Ergod. Th. Dynam. Syst. 6 (1986), 205-239.
Astronom. Phys. 26 (1978), 61-64. 13. R. Mañka, Association and fixed points. Fund. Math. 91 (1976), 105-121. 14. R. D. ), The Scottish Book - Mathematics from the Scottish Café, Birkhauser, Boston, 1981. 15. P. Mine, A fixed point theorem for weakly chainable plane continua, Trans. Amer. Math. Soc. 317 (1990), 303-312. 16. L. Mohler, The fixed point property for homeomorphisms ofl-arcwise connected continua, Proc. Amer. Math. Soc. 52 (1975), 451-456. 17. L. G. Oversteegen, and J. T. , Fixed point free maps on tree-like continua.
We describe results which lead to an analogous theorem for invariant continua (generalized attractors). Mild nondegeneracy and smoothness assumptions replace the strict twist condition in order to assign rotation intervals to attractors for a large class of maps. An orientation-preserving homeomorphism g of the circle has a well-defined rotation number. This number measures the average rate of rotation of a point under iteration by g—averaged, in the limit, over the entire orbit. This limit exists for every point in the circle and is independent of the point chosen.