馬蹄映射(英語:horseshoe map)在混沌理論中是指一類能將一個正方形映射到其自身的混沌映射。該映射最早是由斯蒂芬·斯梅爾在研究范德波爾振盪器時提出的。
在馬蹄映射的作用下,一個正方形通過「壓縮」、「伸長」、「摺疊」的過程後形成馬蹄鐵形狀,並重新成為正方形。馬蹄映射是具有無窮多周期點、結構穩定的動力系統。其動力學性質具有混沌現象的各種典型特徵,是混沌動力系統中的經典模型。
參考文獻
- David Ruelle. What is a strange attractor? (PDF). Notices of the American Mathematical Society. 2006, 53 (7): 764–765 [2016-12-03]. (原始內容存檔 (PDF)於2021-04-28).
- Stephen Smale. Differentiable dynamical systems. Bulletin of the American Mathematical Society. 1967, 73 (6): 747–817. doi:10.1090/S0002-9904-1967-11798-1.
- P. Cvitanović; G. Gunaratne; I. Procaccia. Topological and metric properties of Hénon-type strange attractors. Physical Review A. 1988, 38 (3): 1503–1520. PMID 9900529. doi:10.1103/PhysRevA.38.1503.
- André de Carvalho. Pruning fronts and the formation of horseshoes. Ergodic theory and dynamical systems. 1999, 19 (4): 851–894. doi:10.1017/S0143385799133972.
- André de Carvalho; Toby Hall. How to prune a horseshoe. Nonlinearity. 2002, 15 (3): R19–R68. doi:10.1088/0951-7715/15/3/201.
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