Reversible maps and their symmetry lines |
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| Institution: | 1. Key Laboratory of Numerical Simulation of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan 641112, PR China;2. Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China;1. Courant Institute of Mathematical Sciences, New York University, 251 Street, New York, NY 10012, USA;2. Mathematics department, University of Surrey, Guildford GU2 7XH, United Kingdom |
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| Abstract: | In this paper, we present some methods to determine whether a planar map is reversible. Using these methods, we show that four automorphisms are reversible including Cremona map, cubic Hénon map, Knuth map and McMillan map. Some of them are not polynomial automorphism. We give the recurrence formulas of their symmetry lines, draw their phase portraits and symmetry lines with MATLAB software. Some special properties of their symmetry lines are explained and their beauties are also visually displayed. |
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