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Isolated singularities for elliptic equations with hardy operator and source nonlinearity
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.
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. |






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