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Zeta functions and topological entropy of periodic nonautonomous dynamical systems
1. | Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Instituto Superior Técnico, TUL, Lisboa, Portugal |
2. | Mathematical Institute, Silesian University in Opava, Czech Republic |
References:
[1] |
R. L. Adler, A. G. Konheim and M. H. McAndrew, Topological entropy, Trans. Amer. Math. Soc., 114 (1965), 309-319.
doi: 10.1090/S0002-9947-1965-0175106-9. |
[2] |
Z. AlSharawi, J. Angelos, S. Elaydi and L. Rakesh, An extension of Sharkovsky's theorem to periodic difference equations, J. Math. Anal. Appl., 316 (2006), 128-141.
doi: 10.1016/j.jmaa.2005.04.059. |
[3] |
J. F. Alves and Sousa J. Ramos, Kneading theory for tree maps, Ergodic Theory Dynam. Systems, 24 (2004), 957-985.
doi: 10.1017/S014338570400015X. |
[4] |
J. F. Alves, R. Hric and J. S. Ramos, Topological entropy, homological growth and zeta functions on graphs, Nonlinearity, 18 (2005), 591-607.
doi: 10.1088/0951-7715/18/2/008. |
[5] |
J. F. Alves, What we need to find out the periods of a periodic difference equation, J. Difference Equ. Appl., 15 (2009), 833-847.
doi: 10.1080/10236190802357701. |
[6] |
M. Artin and B. Mazur, On periodic points, Ann. of Math, 81 (1965), 82-99.
doi: 10.2307/1970384. |
[7] |
M. Baillif, Dynamical zeta functions for tree maps, Nonlinearity, 12 (1999), 1511-1529.
doi: 10.1088/0951-7715/12/6/305. |
[8] |
V. Baladi and D. Ruelle, An extension of the theorem of Milnor and Thurston on the zeta functions of interval maps, Ergodic Theory Dynam. Systems, 14 (1994), 621-632.
doi: 10.1017/S0143385700008087. |
[9] |
V. Baladi, Correlation spectrum of quenched and annealed equilibrium states for random expanding maps, Comm. Math. Phys., 186 (1997), 671-700.
doi: 10.1007/s002200050124. |
[10] |
V. Baladi, Periodic orbits and dynamical spectra, Ergodic Theory Dynam. Systems, 18 (1998), 255-292.
doi: 10.1017/S0143385798113925. |
[11] |
J. Buzzi, Some remarks on random zeta functions, Ergodic Theory Dynam. Systems, 22 (2002), 1031-1040.
doi: 10.1017/S0143385702000524. |
[12] |
J. S. Cánovas and A. Linero, Periodic structure of alternating continuous interval maps, J. Difference Equ. Appl., 12 (2006), 847-858.
doi: 10.1080/10236190600772515. |
[13] |
S. Kolyada, M. Misiurewicz and L. Snoha, Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval, Fund. Math, 160 (1999), 161-181. |
[14] |
S. Kolyada and L. Snoha, Topological entropy of nonautonomous dynamical systems, Random Comput. Dynam., 4 (1996), 205-233. |
[15] |
J. Milnor and W. Thurston, "On Iterated Maps of the Interval," Dynamical systems (College Park, MD, 1986-87), 465-563, Lecture Notes in Math, 1342, Springer, Berlin, 1988. |
[16] |
M. Misiurewicz and W. Szlenk, Entropy of piecewise monotone mappings, Studia Math, 67 (1980), 45-63. |
[17] |
D. Ruelle, An extension of the theory of Fredholm determinants, Inst. Hautes Études Sci. Publ. Math, 72 (1990), 175-193.
doi: 10.1007/BF02699133. |
show all references
References:
[1] |
R. L. Adler, A. G. Konheim and M. H. McAndrew, Topological entropy, Trans. Amer. Math. Soc., 114 (1965), 309-319.
doi: 10.1090/S0002-9947-1965-0175106-9. |
[2] |
Z. AlSharawi, J. Angelos, S. Elaydi and L. Rakesh, An extension of Sharkovsky's theorem to periodic difference equations, J. Math. Anal. Appl., 316 (2006), 128-141.
doi: 10.1016/j.jmaa.2005.04.059. |
[3] |
J. F. Alves and Sousa J. Ramos, Kneading theory for tree maps, Ergodic Theory Dynam. Systems, 24 (2004), 957-985.
doi: 10.1017/S014338570400015X. |
[4] |
J. F. Alves, R. Hric and J. S. Ramos, Topological entropy, homological growth and zeta functions on graphs, Nonlinearity, 18 (2005), 591-607.
doi: 10.1088/0951-7715/18/2/008. |
[5] |
J. F. Alves, What we need to find out the periods of a periodic difference equation, J. Difference Equ. Appl., 15 (2009), 833-847.
doi: 10.1080/10236190802357701. |
[6] |
M. Artin and B. Mazur, On periodic points, Ann. of Math, 81 (1965), 82-99.
doi: 10.2307/1970384. |
[7] |
M. Baillif, Dynamical zeta functions for tree maps, Nonlinearity, 12 (1999), 1511-1529.
doi: 10.1088/0951-7715/12/6/305. |
[8] |
V. Baladi and D. Ruelle, An extension of the theorem of Milnor and Thurston on the zeta functions of interval maps, Ergodic Theory Dynam. Systems, 14 (1994), 621-632.
doi: 10.1017/S0143385700008087. |
[9] |
V. Baladi, Correlation spectrum of quenched and annealed equilibrium states for random expanding maps, Comm. Math. Phys., 186 (1997), 671-700.
doi: 10.1007/s002200050124. |
[10] |
V. Baladi, Periodic orbits and dynamical spectra, Ergodic Theory Dynam. Systems, 18 (1998), 255-292.
doi: 10.1017/S0143385798113925. |
[11] |
J. Buzzi, Some remarks on random zeta functions, Ergodic Theory Dynam. Systems, 22 (2002), 1031-1040.
doi: 10.1017/S0143385702000524. |
[12] |
J. S. Cánovas and A. Linero, Periodic structure of alternating continuous interval maps, J. Difference Equ. Appl., 12 (2006), 847-858.
doi: 10.1080/10236190600772515. |
[13] |
S. Kolyada, M. Misiurewicz and L. Snoha, Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval, Fund. Math, 160 (1999), 161-181. |
[14] |
S. Kolyada and L. Snoha, Topological entropy of nonautonomous dynamical systems, Random Comput. Dynam., 4 (1996), 205-233. |
[15] |
J. Milnor and W. Thurston, "On Iterated Maps of the Interval," Dynamical systems (College Park, MD, 1986-87), 465-563, Lecture Notes in Math, 1342, Springer, Berlin, 1988. |
[16] |
M. Misiurewicz and W. Szlenk, Entropy of piecewise monotone mappings, Studia Math, 67 (1980), 45-63. |
[17] |
D. Ruelle, An extension of the theory of Fredholm determinants, Inst. Hautes Études Sci. Publ. Math, 72 (1990), 175-193.
doi: 10.1007/BF02699133. |
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