Geodesic
Random processes generated by a hyperbolic sequence of mappings. II
Izvestiya. Mathematics , Tome 44 (1995) no. 3, pp. 617-627.

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This paper is a direct continuation of . It contains proofs of the theorems announced there on the existence of invariant classes of functional elements and functional deformations for a hyperbolic sequence of mappings, as well as theorems on the existence of invariant cones in spaces of regular functions defined on a set of functional elements. 
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V. I. Bakhtin. Random processes generated by a hyperbolic sequence of mappings. II. Izvestiya. Mathematics , Tome 44 (1995) no. 3, pp. 617-627. http://geodesic.mathdoc.fr/item/IM2_1995_44_3_a8/

[1] V. I. Bakhtin, “Sluchainye protsessy, porozhdennye giperbolicheskoi posledovatelnostyu otobrazhenii. I”, Izv. RAN. Ser. matem., 58:2 (1994), 40–72 | Zbl

[2] G. A. Margulis, “O nekotorykh merakh, svyazannykh s $Y$-potokami na kompaktnykh mnogoobraziyakh”, Funkts. analiz, 4:1 (1970), 62–76 | MR | Zbl

[3] V. I. Bakhtin, “Pryamoi metod postroeniya invariantnoi mery na giperbolicheskom attraktore”, Izv. RAN. Ser. matem., 56:5 (1992), 934–957 | MR | Zbl