Zero topological entropy for C1 generic vector fields

Manseob Lee

Chaos, Solitons & Fractals, 2018, vol. 108, issue C, 104-106

Abstract: In this paper, we show that C1 generically, a vector field X has zero topological entropy if there are a C1 neighborhood U of X and d > 0 such that for every Y∈U and a periodic point p of Y, ∥Pπ(p)Y|Np∥<π(p)d,where π(p) is the period of p, and PY is the linear Poincaré flow associated to Y. This result is a generalization of Arbieto and Morales [1].

Keywords: Topological entropy; Linear Poincaré flow; Scaled linear Poincaré flow; Morse–Smale (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:108:y:2018:i:c:p:104-106

DOI: 10.1016/j.chaos.2018.01.034

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