Topological classification of periodic orbits in Lorenz system<xref rid="cpb_27_8_080501_fn1" ref-type="fn">*</xref> <fn id="cpb_27_8_080501_fn1"><label>*</label> <p>Project supported by the National Natural Science Foundation of China (Grant Nos. 11647085, 11647086, and 11747106), the Applied Basic Research Foundation of Shanxi Province, China (Grant No. 201701D121011), and the Natural Science Research Fund of North University of China (Grant No. XJJ2016036).</p></fn>

Topological classification of periodic orbits in Lorenz system* *

Project supported by the National Natural Science Foundation of China (Grant Nos. 11647085, 11647086, and 11747106), the Applied Basic Research Foundation of Shanxi Province, China (Grant No. 201701D121011), and the Natural Science Research Fund of North University of China (Grant No. XJJ2016036).

Dong Chengwei^†

(color online) (a) Shortest periodic orbit of Lorenz flow found by the variational method; blue line is the loop guess and red line is the periodic orbit. (b) 2D projection of the periodic orbit 01; the sequence of symbols corresponding to the orbit fragments is labeled. The two equilibria S₋ and S₊ are marked with “+”.