Abstract
Although there are plentiful results on the dynamics of monotone mappings, the problem becomes difficult in the non-monotone case. For PM functions (i.e., for piecewise monotone functions), it is known that the non-monotonicity height is an important index to describe their complexity, and the dynamical properties for such functions are complicated when the non-monotonicity height is infinity. In this paper, we consider the non-monotonity height for a general PM function, and give a classification for the non-monotonicity height of those functions. Our results present a full description of their complexity under iteration.
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The authors are very grateful to the reviewers for their careful checking and helpful suggestions.
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This work is supported by the National Science Foundation of China (#12026207), Program for Scientific Research Start-up Funds of Guangdong Ocean University (#060302102005) and the National College Students’ Innovation and Entrepreneurship Training Program (#202110354039).
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This work is supported by the National Science Foundation of China (#12026207), Program for Scientific Research Start-up Funds of Guangdong Ocean University (#060302102005) and the National College Students’ Innovation and Entrepreneurship Training Program (#202110354039).
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Wu, K., Li, L. & Song, W. A classification of non-monotonicity height for piecewise monotone functions (I): increasing case. Aequat. Math. 98, 287–302 (2024). https://doi.org/10.1007/s00010-023-01010-8
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DOI: https://doi.org/10.1007/s00010-023-01010-8