# Coexisting cycles in a class of 3-D discrete maps

ESAIM: Proceedings (2012)

- Volume: 36, page 170-179
- ISSN: 1270-900X

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topAgliari, 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 -

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