ARCS, BALLS AND SPHERES THAT CANNOT BE ATTRACTORS IN R-3

作者:Sanchez Gabites J J*
来源:Transactions of the American Mathematical Society, 2016, 368(5): 3591-3627.
DOI:10.1090/tran/6570

摘要

For any compact set K subset of R-3 we define a number r( K) that is either a nonnegative integer or infinity. Intuitively, r(K) provides some information on how wildly K sits in R-3. We show that attractors for discrete or continuous dynamical systems have finite r and then prove that certain arcs, balls and spheres cannot be attractors by showing that their r is infinite.

  • 出版日期2016-5