Abstract
In this paper we consider the class of three-dimensional discrete maps M (x, y, z) =[ Phi(y) ,Phi(z) , Phi(x)], where Phi: R --> R is an endomorphism. We show that all the cycles of the 3-D map M can be obtained by those of Phi(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 Phi(x) has a cycle of period n>1, 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 eff ect of the fl ip bifurcation of a fi xed point.
Lingua originale | English |
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Titolo della pubblicazione ospite | ESAIM. PROCEEDINGS ECIT 2010 |
Pagine | 170-179 |
Numero di pagine | 10 |
Volume | 36 |
DOI | |
Stato di pubblicazione | Pubblicato - 2012 |
Evento | European Conference on Iteration Theory 2010 - Nant (Francia) Durata: 12 set 2010 → 17 set 2010 |
Convegno
Convegno | European Conference on Iteration Theory 2010 |
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Città | Nant (Francia) |
Periodo | 12/9/10 → 17/9/10 |
Keywords
- 3-D discrete maps
- Bifurcations of co-dimension 3
- Periodic orbits