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Correlation integral and determinism for a family of $2^\infty$ maps
1. | Slovanet a.s., Záhradnícka 151, 821 08 Bratislava, Slovak Republic |
References:
[1] |
L. S. Block and W. A. Coppel, Dynamics in One Dimension, Springer-Verlag, Berlin, 1992. |
[2] |
L. S. Block and J. Keesling, A characterization of adding machine maps, Topology Appl., 140 (2004), 151-161.
doi: 10.1016/j.topol.2003.07.006. |
[3] |
J. P. Boroński and P. Oprocha, On indecomposability in chaotic attractors, Proc. Amer. Math. Soc., 143 (2015), 3659-3670.
doi: 10.1090/S0002-9939-2015-12526-9. |
[4] |
P. Collas and D. Klein, An ergodic adding machine on the Cantor set, Enseign. Math. (2), 40 (1994), 249-266. |
[5] |
J.-P. Delahaye, Fonctions admettant des cycles d'ordre n'importe quelle puissance de $2$ et aucun autre cycle, C. R. Acad. Sci. Paris Sér. A-B, 291 (1980), A323-A325. |
[6] |
R. L. Devaney, An Introduction to Chaotic Dynamical Systems, $2^{nd}$ edition, Addison-Wesley Publishing Company, Advanced Book Program, Redwood City, CA, 1989. |
[7] |
M. Grendár, J. Majerová and V. Špitalský, Strong laws for recurrence quantification analysis, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 23 (2013), 1350147, 13 pp.
doi: 10.1142/S0218127413501472. |
[8] |
P. Grassberger and I. Procaccia, Measuring the strangeness of strange attractors, Phys. D, 9 (1983), 189-208.
doi: 10.1016/0167-2789(83)90298-1. |
[9] |
R. Hric, Topological sequence entropy for maps of the interval, Proc. Amer. Math. Soc., 127 (1999), 2045-2052.
doi: 10.1090/S0002-9939-99-04799-1. |
[10] |
H. Kantz and T. Schreiber, Nonlinear Time Series Analysis, $2^{nd}$ edition, Cambridge University Press, Cambridge, 2004. |
[11] |
M. Misiurewicz, Invariant measures for continuous transformations of $[0,1]$ with zero topological entropy, in Ergodic theory (Proc. Conf., Math. Forschungsinst., Oberwolfach, 1978), Springer, Berlin, 729 (1979), 144-152. |
[12] |
A. Manning and K. Simon, A short existence proof for correlation dimension, J. Statist. Phys., 90 (1998), 1047-1049.
doi: 10.1023/A:1023253709865. |
[13] |
Ya. B. Pesin, On rigorous mathematical definitions of correlation dimension and generalized spectrum for dimensions, J. Statist. Phys., 71 (1993), 529-547.
doi: 10.1007/BF01058436. |
[14] |
Ya. B. Pesin and A. Tempelman, Correlation dimension of measures invariant under group actions, Random Comput. Dynam., 3 (1995), 137-156. |
[15] |
S. Ruette, Chaos for continuous interval maps,, 2003. Available from: , ().
|
[16] |
J. Smítal, Chaotic functions with zero topological entropy, Trans. Amer. Math. Soc., 297 (1986), 269-282.
doi: 10.1090/S0002-9947-1986-0849479-9. |
[17] |
J. P. Zbilut and C. L. Webber Jr., Embeddings and delays as derived from quantification of recurrence plots, Physics Letters A, 171 (1992), 199-203.
doi: 10.1016/0375-9601(92)90426-M. |
show all references
References:
[1] |
L. S. Block and W. A. Coppel, Dynamics in One Dimension, Springer-Verlag, Berlin, 1992. |
[2] |
L. S. Block and J. Keesling, A characterization of adding machine maps, Topology Appl., 140 (2004), 151-161.
doi: 10.1016/j.topol.2003.07.006. |
[3] |
J. P. Boroński and P. Oprocha, On indecomposability in chaotic attractors, Proc. Amer. Math. Soc., 143 (2015), 3659-3670.
doi: 10.1090/S0002-9939-2015-12526-9. |
[4] |
P. Collas and D. Klein, An ergodic adding machine on the Cantor set, Enseign. Math. (2), 40 (1994), 249-266. |
[5] |
J.-P. Delahaye, Fonctions admettant des cycles d'ordre n'importe quelle puissance de $2$ et aucun autre cycle, C. R. Acad. Sci. Paris Sér. A-B, 291 (1980), A323-A325. |
[6] |
R. L. Devaney, An Introduction to Chaotic Dynamical Systems, $2^{nd}$ edition, Addison-Wesley Publishing Company, Advanced Book Program, Redwood City, CA, 1989. |
[7] |
M. Grendár, J. Majerová and V. Špitalský, Strong laws for recurrence quantification analysis, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 23 (2013), 1350147, 13 pp.
doi: 10.1142/S0218127413501472. |
[8] |
P. Grassberger and I. Procaccia, Measuring the strangeness of strange attractors, Phys. D, 9 (1983), 189-208.
doi: 10.1016/0167-2789(83)90298-1. |
[9] |
R. Hric, Topological sequence entropy for maps of the interval, Proc. Amer. Math. Soc., 127 (1999), 2045-2052.
doi: 10.1090/S0002-9939-99-04799-1. |
[10] |
H. Kantz and T. Schreiber, Nonlinear Time Series Analysis, $2^{nd}$ edition, Cambridge University Press, Cambridge, 2004. |
[11] |
M. Misiurewicz, Invariant measures for continuous transformations of $[0,1]$ with zero topological entropy, in Ergodic theory (Proc. Conf., Math. Forschungsinst., Oberwolfach, 1978), Springer, Berlin, 729 (1979), 144-152. |
[12] |
A. Manning and K. Simon, A short existence proof for correlation dimension, J. Statist. Phys., 90 (1998), 1047-1049.
doi: 10.1023/A:1023253709865. |
[13] |
Ya. B. Pesin, On rigorous mathematical definitions of correlation dimension and generalized spectrum for dimensions, J. Statist. Phys., 71 (1993), 529-547.
doi: 10.1007/BF01058436. |
[14] |
Ya. B. Pesin and A. Tempelman, Correlation dimension of measures invariant under group actions, Random Comput. Dynam., 3 (1995), 137-156. |
[15] |
S. Ruette, Chaos for continuous interval maps,, 2003. Available from: , ().
|
[16] |
J. Smítal, Chaotic functions with zero topological entropy, Trans. Amer. Math. Soc., 297 (1986), 269-282.
doi: 10.1090/S0002-9947-1986-0849479-9. |
[17] |
J. P. Zbilut and C. L. Webber Jr., Embeddings and delays as derived from quantification of recurrence plots, Physics Letters A, 171 (1992), 199-203.
doi: 10.1016/0375-9601(92)90426-M. |
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