Conjugacy between piecewise monotonic functions and their iterative roots
It was proved that all continuous functions are topologically conjugate to their continuous iterative roots in monotonic cases. An interesting problem reads： Does the same conclusion hold in non-monotonic cases？We give a negative answer to the problem by presenting a necessary condition for the topo...
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| Veröffentlicht in: | Science China. Mathematics 2016-02, Vol.59 (2), p.367-378 |
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| container_title | Science China. Mathematics |
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| creator | Li, Lin Zhang, WenMeng |
| description | It was proved that all continuous functions are topologically conjugate to their continuous iterative roots in monotonic cases. An interesting problem reads： Does the same conclusion hold in non-monotonic cases？We give a negative answer to the problem by presenting a necessary condition for the topological conjugacy,which helps us construct counter examples. We also give a sufficient condition as well as a method of constructing the topological conjugacy. |
| doi_str_mv | 10.1007/s11425-015-5065-6 |
| format | Article |
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An interesting problem reads： Does the same conclusion hold in non-monotonic cases？We give a negative answer to the problem by presenting a necessary condition for the topological conjugacy,which helps us construct counter examples. We also give a sufficient condition as well as a method of constructing the topological conjugacy.</abstract><cop>Beijing</cop><pub>Science China Press</pub><doi>10.1007/s11425-015-5065-6</doi><tpages>12</tpages></addata></record> |
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| source | SpringerNature Journals; Alma/SFX Local Collection |
| subjects | Applications of Mathematics China Conjugates Construction Functions (mathematics) Iterative methods Mathematical analysis Mathematics Mathematics and Statistics Roots Topology 充分条件 分段线性函数 拓扑共轭 构造反例 连续函数 迭代根 非单调 |
| title | Conjugacy between piecewise monotonic functions and their iterative roots |
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