Delgado, Jorge; Romero, Neptalí; Rovella, Alvaro; Vilamajó, Francesc Bounded solutions of quadratic circulant difference equations. (English) Zbl 1097.37011 J. Difference Equ. Appl. 11, No. 10, 897-907 (2005). Summary: In this paper we develop some techniques to obtain global hyperbolicity for a certain class of endomorphisms of \((\mathbb R^p)^n\) with \(p,n \geq 2\). This kind of endomorphisms are obtained from vectorial difference equations where the mapping defining these equations satisfy a circulant condition. In particular, we show that one-parameter families of these quadratic endomorphisms are hyperbolic for large values of the parameter. Cited in 6 Documents MSC: 37C05 Dynamical systems involving smooth mappings and diffeomorphisms 37D05 Dynamical systems with hyperbolic orbits and sets 39A99 Difference equations Keywords:vectorial difference equation; circulant delay endomorphisms; expanding Cantor set; Euler’s method × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Bofill F., Advanced Nonlinear Studies 4 pp 37– (2004) [2] DOI: 10.1155/S1026022600000492 · doi:10.1155/S1026022600000492 [3] Davis P.J., Circulant Matrices (1979) [4] Delgado, J., Romero, N., Rovella, A., Vilamajó, F., Hyperbolic Real Cellular Automata. To appear in Dynamics of Continuous, Discrete and Impulsive Systems. · Zbl 1089.37005 [5] Kaneko K., Theory and Applications of Coupled Map Lattices (1993) · Zbl 0777.00014 [6] DOI: 10.1142/S0218127499001139 · Zbl 1192.37108 · doi:10.1142/S0218127499001139 [7] DOI: 10.1137/S1111111101395410 · Zbl 1002.37042 · doi:10.1137/S1111111101395410 [8] DOI: 10.1007/s002200050390 · Zbl 0929.37014 · doi:10.1007/s002200050390 [9] DOI: 10.3934/dcdsb.2003.3.409 · Zbl 1152.39303 · doi:10.3934/dcdsb.2003.3.409 [10] DOI: 10.1007/BF02099608 · Zbl 0842.58065 · doi:10.1007/BF02099608 [11] DOI: 10.1080/10236199708808108 · Zbl 0907.39004 · doi:10.1080/10236199708808108 [12] DOI: 10.1142/S0218127493000234 · Zbl 0872.68123 · doi:10.1142/S0218127493000234 [13] DOI: 10.1080/10236190290017487 · Zbl 1005.39015 · doi:10.1080/10236190290017487 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.