RENORMALIZATION OF TWO-DIMENSIONAL PIECEWISE LINEAR MAPS: ABUNDANCE OF 2-D STRANGE ATTRACTORS

Antonio Pumarino; Jose Angel Rodriguez; Enrique Vigil

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RENORMALIZATION OF TWO-DIMENSIONAL PIECEWISE LINEAR MAPS: ABUNDANCE OF 2-D STRANGE ATTRACTORS

机译：二维分段线性映射的重新归一化：二维奇异吸引子的丰度

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摘要

For a two parameter family of two-dimensional piecewise linear maps and for every natural number n, we prove not only the existence of intervals of parameters for which the respective maps are n times renormalizable but also we show the existence of intervals of parameters where the coexistence of at least 2™ strange attractors takes place. This family of maps contains the two-dimensional extension of the classical one-dimensional family of tent maps.

机译：对于二维分段线性映射的两个参数族以及每个自然数n，我们不仅证明了存在各自的映射可以n次重整化的参数的间隔，而且还证明了存在参数间隔的情况至少存在2个奇异吸引子并存。此地图族包含经典一维帐篷地图族的二维扩展。

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来源
《Discrete and continuous dynamical systems》 |2018年第2期|941-966|共26页
作者
Antonio Pumarino; Jose Angel Rodriguez; Enrique Vigil;
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作者单位

Dep. de Matematicas, Universidad de Oviedo Calvo Sotelo s, 33007, Oviedo, Spain;

Dep. de Matematicas, Universidad de Oviedo Calvo Sotelo s, 33007, Oviedo, Spain;

Dep. de Matematicas, Universidad de Oviedo Calvo Sotelo s, 33007, Oviedo, Spain;

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正文语种 eng
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关键词
Piecewise linear maps; renormalization; strange attractor; tent maps;

机译：分段线性图;重新规范化;奇怪的吸引子帐篷地图;

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专利

1. The existence of two-dimensional topologically mixed attractors for some piecewise linear maps of the plane [J] . V. A. Dobrynskii Izvestiya. Mathematics . 1998,第6期

机译：平面的某些分段线性映射的二维拓扑混合吸引子的存在
2. Occurrence of multiple attractor bifurcations in the two-dimensional piecewise linear normal form map [J] . Viktor Avrutin, Michael Schanz, Soumitro Banerjee Nonlinear Dynamics . 2012,第1期

机译：二维分段线性法线形图中的多个吸引子分支的发生
3. Occurrence of multiple attractor bifurcations in the two-dimensional piecewise linear normal form map [J] . Avrutin V., Schanz M., Banerjee S. Nonlinear dynamics . 2012,第1期

机译：二维分段线性法线形图中的多个吸引子分支的发生
4. Circle Like Strange Attractor in a Piecewise Smooth Map [C] . Biswambhar Rakshit, Soumitro Banerjee, Kazuyuki Aihara IFAC Conference on Analysis and Control of Chaotic Systems . 2012

机译：像奇怪的吸引子一样，在分段光滑的地图上
5. Piecewise linear homeomorphisms for approximation of invertible maps. [D] . Groff, Richard E. 2003

机译：分段线性同胚用于近似可逆映射。
6. An Improved Piecewise Linear Chaotic Map Based Image Encryption Algorithm [O] . Yuping Hu, Congxu Zhu, Zhijian Wang -1

机译：一种改进的分段线性混沌映射图像加密算法
7. Renormalization of two-dimensional piecewise linear maps: Abundance of 2-D strange attractors [O] . Pumariño, Antonio, Rodríguez, José Ángel, Vigil, Enrique 2017

机译：二维分段线性映射的重整化：丰度 2-D奇怪的吸引子
8. Chaotic Motion of a Weakly Nonlinear, Modulated Oscillator (Nonlinear Oscillation/Strange Attractor) [R] . Miles, J. 1984

机译：弱非线性调制振子的混沌运动（非线性振荡/奇异吸引子）

RENORMALIZATION OF TWO-DIMENSIONAL PIECEWISE LINEAR MAPS: ABUNDANCE OF 2-D STRANGE ATTRACTORS

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