马蹄映射（英语：horseshoe map）在混沌理论中是指一类能将一个正方形映射到其自身的混沌映射。该映射最早是由斯蒂芬·斯梅尔在研究范德波尔振荡器时提出的。
在马蹄映射的作用下，一个正方形通过“压缩”、“伸长”、“折叠”的过程后形成马蹄铁形状，并重新成为正方形。马蹄映射是具有无穷多周期点、结构稳定的动力系统。其动力学性质具有混沌现象的各种典型特征，是混沌动力系统中的经典模型。
参考文献
- David Ruelle. What is a strange attractor? (PDF). Notices of the American Mathematical Society. 2006, 53 (7): 764–765 [2016-12-03]. （原始内容存档 (PDF)于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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