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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, (1992).
|
[2] |
L. S. Block and J. Keesling, A characterization of adding machine maps,, Topology Appl., 140 (2004), 151.
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.
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.
|
[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).
|
[6] |
R. L. Devaney, An Introduction to Chaotic Dynamical Systems,, $2^{nd}$ edition, (1989).
|
[7] |
M. Grendár, J. Majerová and V. Špitalský, Strong laws for recurrence quantification analysis,, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 23 (2013).
doi: 10.1142/S0218127413501472. |
[8] |
P. Grassberger and I. Procaccia, Measuring the strangeness of strange attractors,, Phys. D, 9 (1983), 189.
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.
doi: 10.1090/S0002-9939-99-04799-1. |
[10] |
H. Kantz and T. Schreiber, Nonlinear Time Series Analysis,, $2^{nd}$ edition, (2004).
|
[11] |
M. Misiurewicz, Invariant measures for continuous transformations of $[0,1]$ with zero topological entropy,, in Ergodic theory (Proc. Conf., 729 (1979), 144.
|
[12] |
A. Manning and K. Simon, A short existence proof for correlation dimension,, J. Statist. Phys., 90 (1998), 1047.
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.
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.
|
[15] |
S. Ruette, Chaos for continuous interval maps,, 2003. Available from: , (). Google Scholar |
[16] |
J. Smítal, Chaotic functions with zero topological entropy,, Trans. Amer. Math. Soc., 297 (1986), 269.
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.
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, (1992).
|
[2] |
L. S. Block and J. Keesling, A characterization of adding machine maps,, Topology Appl., 140 (2004), 151.
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.
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.
|
[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).
|
[6] |
R. L. Devaney, An Introduction to Chaotic Dynamical Systems,, $2^{nd}$ edition, (1989).
|
[7] |
M. Grendár, J. Majerová and V. Špitalský, Strong laws for recurrence quantification analysis,, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 23 (2013).
doi: 10.1142/S0218127413501472. |
[8] |
P. Grassberger and I. Procaccia, Measuring the strangeness of strange attractors,, Phys. D, 9 (1983), 189.
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.
doi: 10.1090/S0002-9939-99-04799-1. |
[10] |
H. Kantz and T. Schreiber, Nonlinear Time Series Analysis,, $2^{nd}$ edition, (2004).
|
[11] |
M. Misiurewicz, Invariant measures for continuous transformations of $[0,1]$ with zero topological entropy,, in Ergodic theory (Proc. Conf., 729 (1979), 144.
|
[12] |
A. Manning and K. Simon, A short existence proof for correlation dimension,, J. Statist. Phys., 90 (1998), 1047.
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.
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.
|
[15] |
S. Ruette, Chaos for continuous interval maps,, 2003. Available from: , (). Google Scholar |
[16] |
J. Smítal, Chaotic functions with zero topological entropy,, Trans. Amer. Math. Soc., 297 (1986), 269.
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.
doi: 10.1016/0375-9601(92)90426-M. |
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