`a`
Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Renormalization of two-dimensional piecewise linear maps: Abundance of 2-D strange attractors
Pages: 941 - 966, Issue 2, February 2018

doi:10.3934/dcds.2018040      Abstract        References        Full text (584.7K)           Related Articles

Antonio Pumariño - Departamento de Matemáticas, Universidad de Oviedo, Calvo Sotelo s/n, 33007 Oviedo, Spain (email)
José Ángel Rodríguez - Dep. de Matemáticas, Universidad de Oviedo, Calvo Sotelo s/n, 33007, Oviedo, Spain (email)
Enrique Vigil - Dep. de Matemáticas, Universidad de Oviedo, Calvo Sotelo s/n, 33007, Oviedo, Spain (email)

1 M. Benedicks and L. Carleson, On iterations of $ 1-ax^2 $ on $(-1, 1)$, Annals of Mathematics, 122 (1985), 1-25.       
2 M. Benedicks and L. Carleson, The dynamics of the Hénon map, Annals of Mathematics, 133 (1991), 73-169.       
3 K. M. Brucks and H. Bruin, Topics from One-Dimensional Dynamics, Cambridge University Press, Cambridge, 2004.       
4 J. Buzzi, Absolutely continuous invariant probability measures for arbitrary expanding piecewise $\mathbbR$-analytic mappings of the plane, Ergodic Theory and Dynamical Systems, 20 (2000), 697-708.       
5 W. de Melo and S. van Strien, One-Dimensional Dynamics, Springer-Verlag, Berlin, 1993.       
6 W. de Melo, Renormalization in one-dimensional dynamics, Journal of Difference Equations and Applications, 17 (2011), 1185-1197.       
7 L. Mora and M. Viana, Abundance of strange attractors, Acta Mathematica, 171 (1993), 1-71.       
8 A. Pumariño and J. A. Rodríguez, Coexistence and Persistence of Strange Attractors, Lecture Notes in Mathematics, 1658, Springer-Verlag, Berlin, 1997.       
9 A. Pumariño, J. A. Rodríguez, J. C. Tatjer and E. Vigil, Piecewise linear bidimensional maps as models of return maps for 3D-diffeomorphisms, in Progress and Challenges in Dynamical Systems, Springer Proc. Math. Stat., 54, Springer, Heidelberg, 2013, 351-366.       
10 A. Pumariño, J. A. Rodríguez, J. C. Tatjer and E. Vigil, Expanding Baker Maps as models for the dynamics emerging from 3D-homoclinic bifurcations, Discrete and Continuous Dynamical Systems - Series B, 19 (2014), 523-541.       
11 A. Pumariño, J. A. Rodríguez, J. C. Tatjer and E. Vigil, Chaotic dynamics for 2-d tent maps, Nonlinearity, 28 (2015), 407-434.       
12 A. Pumariño, J. A. Rodríguez and E. Vigil, Expanding Baker Maps: Coexistence of strange attractors, Discrete and Continuous Dynamical Systems - Series A, 37 (2017), 1651-1678.       
13 A. Pumariño and J. C. Tatjer, Dynamics near homoclinic bifurcations of three-dimensional dissipative diffeomorphisms, Nonlinearity, 19 (2006), 2833-2852.       
14 A. Pumariño and J. C. Tatjer, Attractors for return maps near homoclinic tangencies of three-dimensional dissipative diffeomorphism, Discrete and Continuous Dynamical Systems - Series B, 8 (2007), 971-1005.       
15 S. Sternberg, On the structure of local homeomorphisms of euclidean n-space, American Journal of Mathematics, 80 (1958), 623-631.       
16 J. C. Tatjer, Three-dimensional dissipative diffeomorphisms with homoclinic tangencies, Ergodic Theory and Dynamical Systems, 21 (2001), 249-302.       

Go to top