DCDS-B
Expanding Baker Maps as models for the dynamics emerging from 3D-homoclinic bifurcations
Antonio Pumariño José Ángel Rodríguez Joan Carles Tatjer Enrique Vigil
Discrete & Continuous Dynamical Systems - B 2014, 19(2): 523-541 doi: 10.3934/dcdsb.2014.19.523
For certain 3D-homoclinic tangencies where the unstable manifold of the saddle point involved in the homoclinic tangency has dimension two, many different strange attractors have been numerically observed for the corresponding family of limit return maps. Moreover, for some special value of the parameter, the respective limit return map is conjugate to what was called bidimensional tent map. This piecewise affine map is an example of what we call now Expanding Baker Map, and the main objective of this paper is to show how many of the different attractors exhibited for the limit return maps resemble the ones observed for Expanding Baker Maps.
keywords: Expanding Baker Maps. strange attractors Limit return maps
DCDS
Renormalization of two-dimensional piecewise linear maps: Abundance of 2-D strange attractors
Antonio Pumariño José Ángel Rodríguez Enrique Vigil
Discrete & Continuous Dynamical Systems - A 2018, 38(2): 941-966 doi: 10.3934/dcds.2018040

For a two parameter family of two-dimensional piecewise linear maps and for every natural number $n$, we prove not only the existence of intervals of parameters for which the respective maps are n times renormalizable but also we show the existence of intervals of parameters where the coexistence of at least $2^n$ strange attractors takes place. This family of maps contains the two-dimensional extension of the classical one-dimensional family of tent maps.

keywords: Piecewise linear maps renormalization strange attractor tent maps
DCDS
Renormalizable Expanding Baker Maps: Coexistence of strange attractors
Antonio Pumariño José Ángel Rodríguez Enrique Vigil
Discrete & Continuous Dynamical Systems - A 2017, 37(3): 1651-1678 doi: 10.3934/dcds.2017068

We introduce the concept of Expanding Baker Maps and renormalizable Expanding Baker Maps in a two-dimensional scenario. For a one-parameter family of Expanding Baker Maps we prove the existence of an interval of parameters for which the respective transformation is renormalizable. Moreover, we show the existence of intervals of parameters for which coexistence of strange attractors takes place.

keywords: Piecewise linear maps renormalization strange attractor
DCDS-B
Persistent two-dimensional strange attractors for a two-parameter family of Expanding Baker Maps
Antonio Pumariño José Ángel Rodríguez Enrique Vigil
Discrete & Continuous Dynamical Systems - B 2019, 24(2): 657-670 doi: 10.3934/dcdsb.2018201

We characterize the attractors for a two-parameter class of two-dimensional piecewise affine maps. These attractors are strange attractors, probably having finitely many pieces, and coincide with the support of an ergodic absolutely invariant probability measure. Moreover, we demonstrate that every compact invariant set with non-empty interior contains one of these attractors. We also prove the existence, for each natural number $ n, $ of an open set of parameters in which the respective transformation exhibits at least $ 2^n $ non connected two-dimensional strange attractors each one of them formed by $ 4^n $ pieces.

keywords: Piecewise affine maps strange attractors invariant measures

Year of publication

Related Authors

Related Keywords

[Back to Top]