Entropy charts and bifurcations for Lorenz maps with infinite derivatives

2021 ◽  
Vol 31 (4) ◽  
pp. 043107
Author(s):  
M. Malkin ◽  
K. Safonov
Keyword(s):  
Lorenz Maps

scholarly journals On α-Limit Sets in Lorenz Maps

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1153
Author(s):  
Łukasz Cholewa ◽  
Piotr Oprocha
Keyword(s):  
Topological Entropy ◽  
Dynamical Behavior ◽  
Unimodal Maps ◽  
Limit Sets ◽  
Lorenz Maps ◽  
Provided Examples

The aim of this paper is to show that α-limit sets in Lorenz maps do not have to be completely invariant. This highlights unexpected dynamical behavior in these maps, showing gaps existing in the literature. Similar result is obtained for unimodal maps on [0,1]. On the basis of provided examples, we also present how the performed study on the structure of α-limit sets is closely connected with the calculation of the topological entropy.

Experimental and Simulated Chaotic RLD Circuit Analysis with the Use of Lorenz Maps

2012 ◽  
pp. 403-409 ◽  
Author(s):  
N. A. Gerodimos ◽  
P. A. Daltzis ◽  
M. P. Hanias ◽  
H. E. Nistazakis ◽  
G. S. Tombras
Keyword(s):  
Circuit Analysis ◽  
Lorenz Maps

scholarly journals Topological properties of Lorenz maps derived from unimodal maps

2020 ◽  
Vol 26 (8) ◽  
pp. 1174-1191 ◽  
Author(s):  
Ana Anušić ◽  
Henk Bruin ◽  
Jernej Činč
Keyword(s):  
Topological Properties ◽  
Unimodal Maps ◽  
Lorenz Maps

Explosions in Lorenz maps

2015 ◽  
Vol 76 ◽  
pp. 130-140 ◽  
Author(s):  
Robert Gilmore
Keyword(s):  
Lorenz Maps

Mixing properties in expanding Lorenz maps

2019 ◽  
Vol 343 ◽  
pp. 712-755
Author(s):  
Piotr Oprocha ◽  
Paweł Potorski ◽  
Peter Raith
Keyword(s):  
Mixing Properties ◽  
Lorenz Maps

scholarly journals Monotonicity and non-monotonicity regions of topological entropy for Lorenz-like families with infinite derivatives

2020 ◽  
Vol 5 (2) ◽  
pp. 293-306
Author(s):  
M.I. Malkin ◽  
K.A. Safonov
Keyword(s):  
Normal Form ◽  
Topological Entropy ◽  
Lorenz Attractor ◽  
Homoclinic Loop ◽  
One Dimensional ◽  
Study Behavior ◽  
Saddle Value ◽  
Lorenz Attractors ◽  
Two Parameter ◽  
Lorenz Maps

AbstractWe study behavior of the topological entropy as the function of parameters for two-parameter family of symmetric Lorenz maps Tc,ɛ(x) = (−1 + c|x|1−ɛ) · sgn(x). This is the normal form for splitting the homoclinic loop in systems which have a saddle equilibrium with one-dimensional unstable manifold and zero saddle value. Due to L.P. Shilnikov results, such a bifurcation corresponds to the birth of Lorenz attractor (when the saddle value becomes positive). We indicate those regions in the bifurcation plane where the topological entropy depends monotonically on the parameter c, as well as those for which the monotonicity does not take place. Also, we indicate the corresponding bifurcations for the Lorenz attractors.

scholarly journals Renormalization for Lorenz maps of monotone combinatorial types

2017 ◽  
Vol 39 (1) ◽  
pp. 132-158
Author(s):  
DENIS GAIDASHEV
Keyword(s):  
Critical Point ◽  
A Priori ◽  
Periodic Points ◽  
Unit Interval ◽  
Return Maps ◽  
Lorenz Maps

Lorenz maps are maps of the unit interval with one critical point of order $\unicode[STIX]{x1D70C}>1$ and a discontinuity at that point. They appear as return maps of sections of the geometric Lorenz flow. We construct real a priori bounds for renormalizable Lorenz maps with certain monotone combinatorics and a sufficiently flat critical point, and use these bounds to show existence of periodic points of renormalization, as well as existence of Cantor attractors for dynamics of infinitely renormalizable Lorenz maps.

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