Peer-Reviewed Journal Articles
Edward Neuman, On two bivariate elliptic means, J. Math. Inequal., 11, No.2 (2017), 345-354 http://files.ele-math.com/preprints/jmi-11-30.pdf
Michael Sullivan joint with Kamal M. Adhikari. Further study of simple smale flows using four band templates, Topology Proceedings, Volume 50, 2017 Pages 21-37. Preprint Presentation Published version
Abstract. In this paper, we discuss how to realize a non singular Smale flow with a four band template on 3-sphere. This extends the work done by the second author on Lorenz Smale flows, Bin Yu on realizing Lorenz Like Smale fows on 3-manifold and continues the work of Elizabeth Haynes and the second author on realizing simple Smale fows with a different four band template on 3-sphere.
Abstract. Smale flows on 3-manifolds can have invariant saddle sets that are suspensions of shifts of finite type. We look at Smale flows with chain recurrent sets consisting of an attracting closed orbit a, a repelling closed orbit r and a saddle set that is a suspension of a full n-shift and draw some conclusions about the knotting and linking of a and r. For example, we show for all values of n it is possible for a and r to be unknots. For any even value of n it is possible for a and r to be the Hopf link, a trefoil and meridain, or a figure-8 knot and meridian.
M. Gumus and J. Xu, Some new results related to α-stability, Linear and Multilinear Algebra, 65: 325-340, 2017