Geodesic
Coexisting cycles in a class of 3-D discrete maps
Anna Agliari1
1 Dept. Economic and Social Science, Catholic University, via Emilia Parmense 84, 49100 Piacenza, Italy
ESAIM. Proceedings, Tome 36 (2012), pp. 170-179 Cet article a éte moissonné depuis la source EDP Sciences

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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.
DOI : 10.1051/proc/201236013

Anna Agliari 1

1 Dept. Economic and Social Science, Catholic University, via Emilia Parmense 84, 49100 Piacenza, Italy 
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     author = {Anna Agliari},
     title = {Coexisting cycles in a class of {3-D} discrete maps},
     journal = {ESAIM. Proceedings},
     pages = {170--179},
     year = {2012},
     volume = {36},
     doi = {10.1051/proc/201236013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201236013/}
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Anna Agliari. Coexisting cycles in a class of 3-D discrete maps. ESAIM. Proceedings, Tome 36 (2012), pp. 170-179. doi: 10.1051/proc/201236013

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