Monotonicity of the Lozi family near the tent-maps

Communications in Mathematical Physics

Volumn 198, Issue 2, 1998, Pages 397-406

  Ishii, Yutaka ^a   Sands, Duncan ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b STONY BROOK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032276493     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050482     Document Type: Article

References (10)

1. Brucks, K. and Misiurewicz, M.: Trajectory of the turning point is dense for almost all tent maps. Ergodic Theory Dynamical Systems 16, 1173-1183 (1996)
2. Coven, E.M., Kan, I. and Yorke, J.A.: Pseudo-orbit shadowing in the family of tent maps. Trans. Am. Math. Soc. 308 (1), 227-241 (1988)
3. Cvitanović, P.: Periodic orbits as the skeleton of classical and quantum chaos. Phys.D 5, 138-151 (1991)
4. Cvitanović, P., Gunaratne, G.H., and Procaccia, I.: Topological and metric properties of Hénon-type strange attractors. Phys. Rev. A 38, 1503-1520 (1988)
5. Ishii, Y.: Towards a kneading theory for Lozi mappings I: A solution of the pruning front conjecture and the first tangency problem. Nonlinearity 10, 731-747 (1997)
6. Ishii, Y.: Towards a kneading theory for Lozi mappings II: Monotonicity of the topological entropy and Hausdorff dimension of attractors. Commun. Math. Phys. 190, 375-394 (1997)
7. Lozi, R.: Un attracteur étrange(?) du type attracteur de Hénon. J. Phys. (Paris), 39, 69-77 (1978)
8. Milnor, J. and Thurston, W.: On iterated maps of the interval. In: Dynamical Systems: Proceedings 1986-87, Lecture Notes in Mathematics 1342, Berlin-Heidelberg-New York: Springer-Verlag, 1988, pp. 465-563
9. Misiurewicz, M.: Strange attractors for the Lozi mappings. In: R. G. Helleman, editor, Nonlinear Dynamics, New York: The New York Academy of Sciences, 1980, Volume 357, pp. 348-358
10. Sands, D.: Topological conditions for positive Lyapunov exponent in unimodal maps. Preprint 95-59, Université de Paris-XI (Orsay), 1995