Figure 1.
Positions of some distinguished points
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June
2018, 38(6): 2965-2985.
doi: 10.3934/dcds.2018127
Lozi-like maps
| 1. | Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 N. Blackford Street, Indianapolis, IN 46202, USA |
| 2. | Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10 000 Zagreb, Croatia |
We define a broad class of piecewise smooth plane homeomorphisms which have properties similar to the properties of Lozi maps, including the existence of a hyperbolic attractor. We call those maps Lozi-like. For those maps one can apply our previous results on kneading theory for Lozi maps. We show a strong numerical evidence that there exist Lozi-like maps that have kneading sequences different than those of Lozi maps.
Mathematics Subject Classification:
Primary: 37D45, 37E30; Secondary: 37B10.
Citation:
Michał Misiurewicz, Sonja Štimac. Lozi-like maps. Discrete and Continuous Dynamical Systems,
2018, 38
(6)
: 2965-2985.
doi: 10.3934/dcds.2018127
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References:
| [1] |
M. Brin and G. Stuck, Introduction to Dynamical Systems, Cambridge University Press, Cambridge, 2002. |
| [2] |
Z. Elhadj, Lozi Mappings: Theory and Applications, CRC Press, Boca Raton, FL, 2014. |
| [3] |
Y. Ishii,
Towards a kneading theory for Lozi mappings Ⅰ. A solution of the pruning front conjecture and the first tangency problem, Nonlinearity, 10 (1997), 731-747.
|
| [4] |
R. Lozi,
Un attracteur etrange(?) du type attracteur de Hénon, J. Phys. Colloques(Coll. C5), 39 (1978), 9-10.
doi: 10.1051/jphyscol:1978505. |
| [5] |
M. Misiurewicz,
Strange attractor for the Lozi mappings, Ann. New York Acad. Sci., 357 (1980), 348-358.
|
| [6] |
M. Misiurewicz and S. Štimac,
Symbolic dynamics for Lozi maps, Nonlinearity, 29 (2016), 3031-3046.
doi: 10.1088/0951-7715/29/10/3031. |
show all references
References:
| [1] |
M. Brin and G. Stuck, Introduction to Dynamical Systems, Cambridge University Press, Cambridge, 2002. |
| [2] |
Z. Elhadj, Lozi Mappings: Theory and Applications, CRC Press, Boca Raton, FL, 2014. |
| [3] |
Y. Ishii,
Towards a kneading theory for Lozi mappings Ⅰ. A solution of the pruning front conjecture and the first tangency problem, Nonlinearity, 10 (1997), 731-747.
|
| [4] |
R. Lozi,
Un attracteur etrange(?) du type attracteur de Hénon, J. Phys. Colloques(Coll. C5), 39 (1978), 9-10.
doi: 10.1051/jphyscol:1978505. |
| [5] |
M. Misiurewicz,
Strange attractor for the Lozi mappings, Ann. New York Acad. Sci., 357 (1980), 348-358.
|
| [6] |
M. Misiurewicz and S. Štimac,
Symbolic dynamics for Lozi maps, Nonlinearity, 29 (2016), 3031-3046.
doi: 10.1088/0951-7715/29/10/3031. |
Figure 2.
The set of parameters
Figure 3.
The triangle $\Theta$ and positions of some distinguished points
Figure 4.
Attractor for the Lozi map with parameters described by (F1') and (F2'). The $y$ -coordinate is stretched by factor $7/4$
Figure 5.
Graphs of (F1') and (F2')
Figure 6.
Equations (F1') and (F2') as inequalities
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