標題: Stretches across for chaos
作者: Li, Ming-Chia
應用數學系
Department of Applied Mathematics
公開日期: 1-May-2019
摘要: In 2001, Kennedy et al. [Amer. Math. Mon. 108, 411-423 (2001) and Trans. Amer. Math. Soc. 353, 2513-2530 (2001)] showed a chaos lemma and stated the pseudoconjecture "stretches across implies existence of an invariant set." In this paper, we give a suitable definition of stretches across in topological sense so that the conjecture has an affirmative answer. More precisely, we show that there must be an orbit through a sequence of stretches across. In particular, a closed loop of stretches across implies existence of a periodic orbit. We also give the geometric meaning of stretches across and its relation with the global implicit function theorem.
URI: http://dx.doi.org/10.1063/1.5091451
http://hdl.handle.net/11536/152235
ISSN: 1054-1500
DOI: 10.1063/1.5091451
期刊: CHAOS
Volume: 29
Issue: 5
起始頁: 0
結束頁: 0
Appears in Collections:Articles