References
- R. Abu-Saris, On the periodicity of the difference equation xn+1=α|xn|+βxn−1, J. Differ. Equ. Appl. 5 (1999), pp. 57–69.
- R. Abu-Saris and F. Allan, Periodic and Nonperiodic Solutions of the Difference Equation xn+1=max{xn2,A}xnxn−1, Advances in Difference Equations (Veszprem, 1995), Gordon and Breach, Amsterdam, 1997, pp. 9–17.
- D. Baptista, R. Severino, and S. Vinagre, The basin of attraction of Lozi mappings, Int. J. Bifurcat. Chaos 19 (2009), pp. 1043–1049.
- A.F. Beardon, S.R. Bullet, and P.J. Rippon, Periodic orbits of difference equations, Proc. R. Soc. Edinburgh 125A (1995), pp. 657–674.
- M. Benedicks and L. Carleson, The dynamics of the Hénon map, Ann. Math. 133 (1991), pp. 73–169.
- V. Botella-Soler, J.M. Castelo, J.A. Oteo, and J. Ros, Bifurcations in the Lozi map, J. Phys. A: Math. Theor. 44 (2011), p. Art. ID 305101, 14 pages.
- M. Crampin, Piecewise linear recurrence relations, Math. Gazette 76 (1992), pp. 355–359.
- R.L. Devaney, A piecewise linear model for the zones of instability of an area-preserving map, Phys. 10D (1984), pp. 387–393.
- S. Elaydi, An Introduction to Difference Equations, Springer, New York, 2005.
- Z. Elhadj, Lozi Mappings, Theory and Applications, Taylor & Francis, CRC Press, Boca Raton, FL, 2014.
- J. Feuer, Periodic solutions of the Lyness max equation, J. Math. Anal. Appl 288 (2003), pp. 147–160.
- E.A. Grove and G. Ladas, Periodicities in Nonlinear Difference Equations, Chapman & Hall, CRC Press, Boca Raton, FL, 2005.
- M. Hénon, A two dimensional mapping with a strange attractor, Commun. Math. Phys. 50 (1976), pp. 69–77.
- A. Linero-Bas and D. Nieves-Roldán, A survey on max-type equations, in Advances in Discrete Dynamical Systems, S. Elaydi, S. Kalabušić, and M. Kulenović, eds., Difference Equations, and Applications, Proceedings of the International Conference on Difference Equations and Applications, ICDEA 2021, Springer, Sarajevo, 2021 (in press).
- E.N. Lorenz, Deterministic nonperiodic flow, J. Atmos. Sci. 20 (1963), pp. 130–141.
- R. Lozi, Un attracteur étrange du type attracteur de Hénon, J. Phys. 39 (1978), pp. 9–10.
- M. Misiurewicz, Strange attractor for the Lozi mapping, in Non-linear Dynamics, Annals of the New York Academy of Sciences, Vol. 357, 1980, pp. 348–358.
- E. Ott, Chaos in Dynamical Systems, Cambridge University Press, New York, 1993.
- D. Ruelle and F. Takens, On the nature of turbulence, Commun. Math. Phys. 20 (1971), pp. 167–192.