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Global linearization of periodic difference equations

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  • We deal with $m$-periodic, $n$-th order difference equations and study whether they can be globally linearized. We give an affirmative answer when $m=n+1$ and for most of the known examples appearing in the literature. Our main tool is a refinement of the Montgomery-Bochner Theorem.
    Mathematics Subject Classification: Primary: 39A05; Secondary: 39A20, 39B12.

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  • [1]

    R. M. Abu-Saris and Q. M. Al-Hassan, On global periodicity of difference equations, J. Math. Anal. Appl., 283 (2003), 468-477.doi: 10.1016/S0022-247X(03)00272-5.

    [2]

    K. I. T. Al-Dosary, Global periodicity: An inverse problem, Appl. Math. Lett., 18 (2005), 1041-1045.doi: 10.1016/j.aml.2003.12.010.

    [3]

    F. Balibrea and A. Linero, Some new results and open problems on periodicity of difference equations, in "Iteration Theory" (ECIT '04), Grazer Math. Ber., 350, Karl-Franzens-Univ. Graz, Graz, (2006), 15-38.

    [4]

    F. Balibrea and A. Linero, On the global periodicity of some difference equations of third order, J. Difference Equ. Appl., 13 (2007), 1011-1027.doi: 10.1080/10236190701388518.

    [5]

    F. Balibrea, A. Linero Bas, G. Soler López and S. Stević, Global periodicity of $x_{n+k+1}=f_k(x_{n+k})...f_2(x_ {n+2})f_1(x_{x+1})$, J. Difference Equ. Appl., 13 (2007), 901-910.doi: 10.1080/10236190701351144.

    [6]

    R. H. Bing, A homeomorphism between the $3$-sphere and the sum of two solid horned spheres, Ann. of Math. (2), 56 (1952), 354-362.doi: 10.2307/1969804.

    [7]

    R. H. Bing, Inequivalent families of periodic homeomorphisms of $E_3$, Ann. of Math. (2), 80 (1964), 78-93.doi: 10.2307/1970492.

    [8]

    J. S. Cánovas, A. Linero and G. Soler, A characterization of $k$-cycles, Nonlinear Anal., 72 (2010), 364-372.doi: 10.1016/j.na.2009.06.070.

    [9]

    A. Cima, A. Gasull and V. Mañosa, Global periodicity and complete integrability of discrete dynamical systems, J. Difference Equ. Appl., 12 (2006), 697-716.doi: 10.1080/10236190600703031.

    [10]

    A. Cima, A. Gasull and F. Mañosas, On periodic rational difference equations of order $k$, J. Difference Equ. and Appl., 10 (2004), 549-559.doi: 10.1080/10236190410001667977.

    [11]

    A. Cima, A. Gasull and F. MañosasOn Coxeter recurrences, J. Difference Equ. Appl., to appear.

    [12]

    P. E. Conner and E. E. Floyd, On the construction of periodic maps without fixed points, Proc. Amer. Math. Soc., 10 (1959), 354-360.doi: 10.1090/S0002-9939-1959-0105115-X.

    [13]

    A. Constantin and B. Kolev, The theorem of Kerékjártó on periodic homeomorphisms of the disc and the sphere, Enseign. Math. (2), 40 (1994), 193-204.

    [14]

    H. S. M. Coxeter, Frieze patterns, Acta Arith., 18 (1971), 297-310.

    [15]

    M. Csörnyei and M. Laczkovich, Some periodic and non-periodic recursions, Monatshefte für Mathematik, 132 (2001), 215-236.doi: 10.1007/s006050170042.

    [16]

    R. Haynes, S. Kwasik, J. Mast and R. Schultz, Periodic maps on $\R^7$ without fixed points, Math. Proc. Cambridge Philos. Soc., 132 (2002), 131-136.

    [17]

    J. M. Kister, Differentiable periodic actions on $E^8$ without fixed points, Amer. J. Math., 85 (1963), 316-319.doi: 10.2307/2373217.

    [18]

    M. Kuczma, B. Choczewski and R. Ger, "Iterative Functional Equations," Encyclopedia of Mathematics and its Applications, 32, Cambridge University Press, Cambridge, 1990.

    [19]

    R. P. Kurshan and B. Gopinath, Recursively generated periodic sequences, Canad. J. Math., 26 (1974), 1356-1371.doi: 10.4153/CJM-1974-129-6.

    [20]

    B. D. Mestel, On globally periodic solutions of the difference equation $x_{n+1}=f(x_n)$/$x_{n-1}$, J. Difference Equations and Appl., 9 (2003), 201-209.doi: 10.1080/1023619031000061061.

    [21]

    D. Montgomery and L. Zippin, "Topological Transformation Groups,'' Interscience Publishers, New-York-London, 1955.

    [22]

    R. Plastock, Homeomorphisms between Banach spaces, Transactions of the American Mathematical Society, 200 (1974), 169-183.doi: 10.1090/S0002-9947-1974-0356122-6.

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