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Fractional iterates for \(n\)-dimensional maps. (English) Zbl 1083.39502
Summary: This paper constitutes an extension of results of the author’s paper [Int. J. Bifurcation Chaos Appl. Sci. Eng. 6, No. 1, 55–67 (1996; Zbl 0872.39011)]. We study here the solutions of the problem of the fractional iteration for \(n\)-dimensional maps.

39B12 Iteration theory, iterative and composite equations
39B62 Functional inequalities, including subadditivity, convexity, etc.
37B99 Topological dynamics
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[1] Cathala, J.-C., Multiconnected chaotic areas in the second order endomorphisms, Int. J. system sci., 21, 5, 863-887, (1990) · Zbl 0706.58025
[2] Gradini, L., Some global bifurcations of two-dimensional endomorphisms by use of critical lines, Nonlinear anal. theory, meth. appl., 18, 4, 361-399, (1991)
[3] Lojasiewicz, S., Solution générale de l’équation fonctionelle ƒ(ƒ(… ƒ (x) …)) = g(x), Ann. soc. polon. math., 24, 88-91, (1951) · Zbl 0047.11401
[4] Mira, C., 1990. Private communication.
[5] Mira, C.; Narayaninsamy, T., On two behaviours of two dimensional endomorphisms, Role of the critical curves, Int. J. bifurcations chaos, 3, 1, 187-194, (1993) · Zbl 0870.58079
[6] Mullenbach, S., Contribution à l’itération de l’itération fractionnaire des endomorphismes, ()
[7] Narayaninsamy, T., Contribution à l’étude de l’itération fractionaire et à celle des endomorphismes bi-dimensionnels, Thèse de doctorat de L’université paul sabatier de Toulouse, mathématiques appliquées, no. 1295, (1992)
[8] Narayaninsamy, T., On a class of fractional iterates, Int. J. bifurcations chaos, 6, 1, 55-67, (1996) · Zbl 0872.39011
[9] Narayaninsamy, T., 1997, in preparation.
[10] Zimmerman, G., Uber die existenz iteration wurzeln von abbildungen, ()
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