On the asymptotic properties of piecewise contracting maps
On the asymptotic properties of piecewise contracting maps
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DOI：
10.1080/14689367.2015.1068274
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发表时间：
2011-08
期刊：
影响因子：
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通讯作者：
E. Catsigeras;P. Guiraud;A. Meyroneinc;Edgardo Ugalde
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文献类型：
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作者：
E. Catsigeras;P. Guiraud;A. Meyroneinc;Edgardo Ugalde
摘要 我们对分段收缩映射的渐近动力学现象学感兴趣。我们考虑一类广泛的此类映射，并给出足够的条件来确保一些一般的基本属性，例如吸引子的周期性、完全不连通性或零勒贝格测度。这些条件特别表明非周期性吸引子必然包含映射的不连续性。在这个假设下，我们获得了许多吸引子的例子，从有限的到连通的和混沌的，与迄今为止观察到的（准）周期性渐近行为形成鲜明对比。
ABSTRACT We are interested in the phenomenology of the asymptotic dynamics of piecewise contracting maps. We consider a wide class of such maps and we give sufficient conditions to ensure some general basic properties, such as the periodicity, the total disconnectedness or the zero Lebesgue measure of the attractor. These conditions show in particular that a non-periodic attractor necessarily contains discontinuities of the map. Under this hypothesis, we obtain numerous examples of attractors, ranging from finite to connected and chaotic, contrasting with the (quasi-)periodic asymptotic behaviours observed so far.