Coexisting cycles in a class of 3-D discrete maps

Agliari, Anna. Fournier-Prunaret, D., Gardini, L., and Reich, L., eds. " Coexisting cycles in a class of 3-D discrete maps ." ESAIM: Proceedings 36 (2012): 170-179. <http://eudml.org/doc/251212>.

@article{Agliari2012,
abstract = {In this paper we consider the class of three-dimensional discrete maps M (x, y, z) = [φ(y), φ(z), φ(x)], where φ : ℝ → ℝ is an endomorphism. We show that all the cycles of the 3-D map M can be obtained by those of φ(x), as well as their local bifurcations. In particular we obtain that any local bifurcation is of co-dimension 3, that is three eigenvalues cross simultaneously the unit circle. As the map M exhibits coexistence of cycles when φ(x) has a cycle of period n ≥ 2, making use of the Myrberg map as endomorphism, we describe the structure of the basins of attraction of the attractors of M and we study the effect of the flip bifurcation of a fixed point.},
author = {Agliari, Anna},
editor = {Fournier-Prunaret, D., Gardini, L., Reich, L.},
journal = {ESAIM: Proceedings},
keywords = {3-D discrete maps; Periodic orbits; Bifurcations of co-dimension 3; periodic orbits; bifurcations of co-dimension 3},
language = {eng},
month = {8},
pages = {170-179},
publisher = {EDP Sciences},
title = { Coexisting cycles in a class of 3-D discrete maps },
url = {http://eudml.org/doc/251212},
volume = {36},
year = {2012},
}

TY - JOUR
AU - Agliari, Anna
AU - Fournier-Prunaret, D.
AU - Gardini, L.
AU - Reich, L.
TI - Coexisting cycles in a class of 3-D discrete maps
JO - ESAIM: Proceedings
DA - 2012/8//
PB - EDP Sciences
VL - 36
SP - 170
EP - 179
AB - In this paper we consider the class of three-dimensional discrete maps M (x, y, z) = [φ(y), φ(z), φ(x)], where φ : ℝ → ℝ is an endomorphism. We show that all the cycles of the 3-D map M can be obtained by those of φ(x), as well as their local bifurcations. In particular we obtain that any local bifurcation is of co-dimension 3, that is three eigenvalues cross simultaneously the unit circle. As the map M exhibits coexistence of cycles when φ(x) has a cycle of period n ≥ 2, making use of the Myrberg map as endomorphism, we describe the structure of the basins of attraction of the attractors of M and we study the effect of the flip bifurcation of a fixed point.
LA - eng
KW - 3-D discrete maps; Periodic orbits; Bifurcations of co-dimension 3; periodic orbits; bifurcations of co-dimension 3
UR - http://eudml.org/doc/251212
ER -