Lemmens, Bas and van Gaans, Onno (2009) Dynamics of non-expansive maps on strictly convex normed spaces. Israel Journal of Mathematics, 171 (1). pp. 425-445. ISSN 0021-2172. (doi:https://doi.org/10.1007/s11856-009-0057-2) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)
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This paper concerns the dynamics of non-expansive maps on strictly convex finite dimensional normed spaces. By using results of Edelstein and Lyubich, we show that if X = (a"e (n) , ayen center dot ayen) is strictly convex and X has no 1-complemented Euclidean plane, then every bounded orbit of a non-expansive map f: X -> X, converges to a periodic orbit. By putting extra assumptions on the derivatives of the norm, we also show that the period of each periodic point of a non-expansive map f: X -> X is the order, or, twice the order of a permutation on n letters. This last result generalizes a theorem of Sine, who proved it for a"" (p) (n) where 1 < p < a and p not equal 2. To obtain the results we analyze the ranges of non-expansive projections, the geometry of 1-complemented subspaces, and linear isometries on 1-complemented subspaces.
|Subjects:||Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus|
|Depositing User:||Bas Lemmens|
|Date Deposited:||17 Nov 2011 16:18 UTC|
|Last Modified:||23 May 2014 15:34 UTC|
|Resource URI:||https://kar.kent.ac.uk/id/eprint/28444 (The current URI for this page, for reference purposes)|