Logistic map potentials

被引：9

作者：

Curtright, Thomas ^{[1
]}

Veitia, Andrzej ^{[1
]}

机构：

[1] Univ Miami, Dept Phys, Coral Gables, FL 33124 USA

来源：

PHYSICS LETTERS A | 2011年 / 375卷 / 03期

基金：

美国国家科学基金会;

关键词：

We thank David Fairlie; Xiang Jin; Luca Mezincescu; and especially Cosmas Zachos; for sharing their thoughts about functional evolution methods. One of us (T.C.) thanks the CERN Theoretical Physics Group for its gracious hospitality and generous support. The numerical calculations and graphics in this Letter were made using Maple ®; Mathematica; ®; and MuPAD ® . This work was supported by NSF Award 0855386;

D O I：

10.1016/j.physleta.2010.11.019

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We develop and illustrate methods to compute all single particle potentials that underlie the logistic map, x bar right arrow sx(1 - x) for 0 < s <= 4. We show that the switchback potentials can be obtained from the primary potential through functional transformations. We are thereby able to produce the various branches of the corresponding analytic potential functions, which have an infinite number of branch points for generic s > 2. We illustrate the methods numerically for the cases s = 5/2 and s = 10/3. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：276 / 282

页数：7