-
Previous Article
Central limit theorem for stationary products of toral automorphisms
- DCDS Home
- This Issue
-
Next Article
Periodic and subharmonic solutions for duffing equation with a singularity
Global linearization of periodic difference equations
1. | Dept. de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C, 08193 Bellaterra, Barcelona, Spain, Spain |
2. | Dept. de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C, 08193 Bellaterra, Barcelona |
References:
[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. Mañosas, On 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. |
show all references
References:
[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. Mañosas, On 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. |
[1] |
Małgorzata Migda, Ewa Schmeidel, Małgorzata Zdanowicz. Periodic solutions of a $2$-dimensional system of neutral difference equations. Discrete and Continuous Dynamical Systems - B, 2018, 23 (1) : 359-367. doi: 10.3934/dcdsb.2018024 |
[2] |
Yoshihiro Hamaya. Stability properties and existence of almost periodic solutions of volterra difference equations. Conference Publications, 2009, 2009 (Special) : 315-321. doi: 10.3934/proc.2009.2009.315 |
[3] |
John Erik Fornæss. Periodic points of holomorphic twist maps. Discrete and Continuous Dynamical Systems, 2005, 13 (4) : 1047-1056. doi: 10.3934/dcds.2005.13.1047 |
[4] |
B. Fernandez, E. Ugalde, J. Urías. Spectrum of dimensions for Poincaré recurrences of Markov maps. Discrete and Continuous Dynamical Systems, 2002, 8 (4) : 835-849. doi: 10.3934/dcds.2002.8.835 |
[5] |
Anatoli F. Ivanov, Sergei Trofimchuk. Periodic solutions and their stability of a differential-difference equation. Conference Publications, 2009, 2009 (Special) : 385-393. doi: 10.3934/proc.2009.2009.385 |
[6] |
Grzegorz Graff, Michał Misiurewicz, Piotr Nowak-Przygodzki. Periodic points of latitudinal maps of the $m$-dimensional sphere. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 6187-6199. doi: 10.3934/dcds.2016070 |
[7] |
Chris Bernhardt. Vertex maps for trees: Algebra and periods of periodic orbits. Discrete and Continuous Dynamical Systems, 2006, 14 (3) : 399-408. doi: 10.3934/dcds.2006.14.399 |
[8] |
Xiaoyan Lin, Xianhua Tang. Solutions of nonlinear periodic Dirac equations with periodic potentials. Discrete and Continuous Dynamical Systems - S, 2019, 12 (7) : 2051-2061. doi: 10.3934/dcdss.2019132 |
[9] |
V. Afraimovich, Jean-René Chazottes, Benoît Saussol. Pointwise dimensions for Poincaré recurrences associated with maps and special flows. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 263-280. doi: 10.3934/dcds.2003.9.263 |
[10] |
Weiwei Ding, Xing Liang, Bin Xu. Spreading speeds of $N$-season spatially periodic integro-difference models. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 3443-3472. doi: 10.3934/dcds.2013.33.3443 |
[11] |
Jean Mawhin. Periodic solutions of second order Lagrangian difference systems with bounded or singular $\phi$-Laplacian and periodic potential. Discrete and Continuous Dynamical Systems - S, 2013, 6 (4) : 1065-1076. doi: 10.3934/dcdss.2013.6.1065 |
[12] |
Daniel Wilczak, Piotr Zgliczyński. Topological method for symmetric periodic orbits for maps with a reversing symmetry. Discrete and Continuous Dynamical Systems, 2007, 17 (3) : 629-652. doi: 10.3934/dcds.2007.17.629 |
[13] |
Àngel Jorba, Pau Rabassa, Joan Carles Tatjer. Superstable periodic orbits of 1d maps under quasi-periodic forcing and reducibility loss. Discrete and Continuous Dynamical Systems, 2014, 34 (2) : 589-597. doi: 10.3934/dcds.2014.34.589 |
[14] |
Peter Giesl, Martin Rasmussen. A note on almost periodic variational equations. Communications on Pure and Applied Analysis, 2011, 10 (3) : 983-994. doi: 10.3934/cpaa.2011.10.983 |
[15] |
Dixiang Cheng, Zhengrong Liu, Xin Huang. Periodic solutions of a class of Newtonian equations. Communications on Pure and Applied Analysis, 2009, 8 (6) : 1795-1801. doi: 10.3934/cpaa.2009.8.1795 |
[16] |
Vincenzo Ambrosio, Giovanni Molica Bisci. Periodic solutions for nonlocal fractional equations. Communications on Pure and Applied Analysis, 2017, 16 (1) : 331-344. doi: 10.3934/cpaa.2017016 |
[17] |
Massimiliano Berti, M. Matzeu, Enrico Valdinoci. On periodic elliptic equations with gradient dependence. Communications on Pure and Applied Analysis, 2008, 7 (3) : 601-615. doi: 10.3934/cpaa.2008.7.601 |
[18] |
Daniele Cassani, Antonio Tarsia. Periodic solutions to nonlocal MEMS equations. Discrete and Continuous Dynamical Systems - S, 2016, 9 (3) : 631-642. doi: 10.3934/dcdss.2016017 |
[19] |
Tomás Caraballo, David Cheban. Almost periodic and asymptotically almost periodic solutions of Liénard equations. Discrete and Continuous Dynamical Systems - B, 2011, 16 (3) : 703-717. doi: 10.3934/dcdsb.2011.16.703 |
[20] |
Xianhua Huang. Almost periodic and periodic solutions of certain dissipative delay differential equations. Conference Publications, 1998, 1998 (Special) : 301-313. doi: 10.3934/proc.1998.1998.301 |
2021 Impact Factor: 1.588
Tools
Metrics
Other articles
by authors
[Back to Top]