GLOBAL ATTRACTORS IN THE PARAMETRIZED HENON-DEVANEY MAP

被引：0

作者：

Leal, Bladismir ^{[1
,2
]}

Munoz, Sergio ^{[3
]}

机构：

[1] Univ Tecn Manabi, Inst Ciencias Basicas, Ave Jose Maria Urbina, Portoviejo, Ecuador

[2] Univ Nacl Chimborazo, Fac Ingn, Via Guano Km 1-5, Riobamba, Ecuador

[3] Univ Estado Rio de Janeiro, Fac Tecnol, Dept Matemat Fis & Comp, Resende, Brazil

来源：

REVISTA DE LA UNION MATEMATICA ARGENTINA | 2023年 / 65卷 / 01期

关键词：

Parametrized Henon-Devaney map; non-bounded attractors; invariant non-compact sets; Cantor sets;

D O I：

10.33044/revuma.2133

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given two positive real numbers a and c, we consider the (two-parameter) family of nonlinear mappings F-a,F-c(x, y) = (ax + 1/y, cy - c/y- acx). F-1,F-1 is the classical He'non-Devaney map. For a large region of parameters, we exhibit an invariant non-bounded closed set with fractal structure which is a global attractor. Our approach leads to an in-depth understanding of the He'non-Devaney map and its perturbations.

引用

页码：79 / 101

页数：23

共 8 条

[1] THE BAKER TRANSFORMATION AND A MAPPING ASSOCIATED TO THE RESTRICTED 3 BODY PROBLEM
DEVANEY, RL
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1981, 80 (04) : 465 - 476
[2] Henon M., 2001, LECT NOTES PHYS NEW, V65
[3] Invariant Cantor sets in the parametrized Henon-Devaney map
Leal, Bladismir
Munoz, Sergio
[J]. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2022, 37 (01): : 105 - 126
[4] Henon-Devaney like maps
Leal, Bladismir
Munoz, Sergio
[J]. NONLINEARITY, 2021, 34 (05) : 2878 - 2896
[5] FAMILIES OF TRANSITIVE MAPS ON R WITH HORIZONTAL ASYMPTOTES
Leal, Bladismir
Mata, Guelvis
Munoz, Sergio
[J]. REVISTA DE LA UNION MATEMATICA ARGENTINA, 2018, 59 (02): : 375 - 387
[6] Lenarduzzi F., 2016, THESIS IMPA RIO DE J
[7] RECODING THE CLASSICAL HENON-DEVANEY MAP
Lenarduzzi, Fernando
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2020, 40 (07) : 4073 - 4092
[8] ROBUST TRANSITIVITY OF MAPS OF THE REAL LINE
Munoz, Sergio
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2015, 35 (03) : 1163 - 1177

← 1 →