<abstract xmlns="http://www.w3.org/1999/xhtml">We study behavior of the topological entropy as the function of parameters for two-parameter family of symmetric Lorenz maps <italic>T</italic><italic>c,ɛ</italic>(<italic>x</italic>) = (−1 + <italic>c|x|</italic>1−<italic>ɛ</italic>) · <italic>sgn</italic>(<italic>x</italic>). 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 <italic>c</italic>, as well as those for which the monotonicity does not take place. Also, we indicate the corresponding bifurcations for the Lorenz attractors.</abstract>

We 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.

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

Lobachevsky State University of Nizhniy Novgorod

National Research University Higher School of Economics

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

We 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)....

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

Published Online: Nov 16, 2020

Page range: 293 - 306

Received: Jan 08, 2020

Accepted: Apr 11, 2020

DOI: https://doi.org/10.2478/amns.2020.2.00052

Keywords
topological entropy, Lorenz attractor, homoclinic bifurcation, jump of entropy

© 2020 M.I. Malkin et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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

Published Online: Nov 16, 2020

Page range: 293 - 306

Received: Jan 08, 2020

Accepted: Apr 11, 2020

DOI: https://doi.org/10.2478/amns.2020.2.00052

Keywordstopological entropy, Lorenz attractor, homoclinic bifurcation, jump of entropy

© 2020 M.I. Malkin et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
topological entropy, Lorenz attractor, homoclinic bifurcation, jump of entropy