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Chain transitive induced interval maps on continua
1. | University of Toronto, Bahen Centre 40 St. George St., Room 6290, Toronto, ON, M5S 2E4, Canada |
2. | Institute of Mathematics, NASU, Tereshchenkivs'ka 3, 01601, Kyiv, Ukraine |
References:
[1] |
G. Acosta, A. Illanes and H. Méndez-Lango, The transitivity of induced maps, Topology Appl., 156 (2009), 1013-1033.
doi: 10.1016/j.topol.2008.12.025. |
[2] |
E. Akin, Countable metric spaces and chain transitivity, preprint, 2013. |
[3] |
S. J. Agronsky, A. M. Bruckner, J. G. Ceder and T. L. Pearson, The structure of $\omega$-limit sets for continuous maps,, Real Analysis Exchange, 15 (): 1989.
|
[4] |
A. D. Barwell, C. Good, P. Oprocha and B. E. Raines, Characterizations of $\omega$-limit sets in topologically hyperbolic systems, Discrete Contin. Dyn. Syst., 33 (2013), 1819-1833.
doi: 10.3934/dcds.2013.33.1819. |
[5] |
L. S. Block and W. A. Coppel, Dynamics in One Dimension, Lecture Notes in Mathematics, Vol. 1513, Berlin Heidelberg, Springer-Verlag, 1992. |
[6] |
L. Block and E. Coven, Maps of the interval with every point chain recurrent, Proc. Amer. Math. Soc., 98 (1986), 513-515.
doi: 10.1090/S0002-9939-1986-0857952-8. |
[7] |
L. Block and J. Franke, The chain recurrent set, attractors, and explosions, Ergodic Theory Dynamical Systems, 5 (1985), 321-327.
doi: 10.1017/S0143385700002972. |
[8] |
A. M. Bruckner and J. Smital, The structure of $\omega$-limit sets for continuous maps of the interval, Math. Bohemica, 117 (1992), 42-47. |
[9] |
Y. N. Dowker and F. G. Friedlander, On limit sets in dynamical systems, Proc. London Math. Soc. (3), 4 (1954), 168-176. |
[10] |
V. V. Fedorenko, Asymptotic periodicity of the trajectories of an interval, Ukrainian Math. J., 61 (2009), 854-858.
doi: 10.1007/s11253-009-0238-5. |
[11] |
V. V. Fedorenko, E. Yu. Romanenko and A. N. Sharkovsky, Trajectories of intervals in one-dimensional dynamical systems, J. Difference Equ. Appl., 13 (2007), 821-828.
doi: 10.1080/10236190701396636. |
[12] |
A. Illanes and S. B. Nadler, Jr., Hyperspaces. Fundamentals and Recent Advances, Monographs and Textbooks in Pure and Applied Mathematics, 216, Marcel Dekker, Inc., New York, 1999. |
[13] |
M. Hurley, Chain recurrence and attraction in non-compact spaces, Ergod. Th. & Dynam. Sys., 11 (1991), 709-729.
doi: 10.1017/S014338570000643X. |
[14] |
S. Kolyada and D. Robatian, On omega-limit sets of triangular induced maps, Real Analysis Exchange, 38 (2013), 299-316. |
[15] |
S. Kolyada and L. Snoha, On $\omega$-limit sets of triangular maps,, Real Analysis Exchange, 18 (): 1992.
|
[16] |
D. Kwietniak and P. Oprocha, Topological entropy and chaos for maps induced on hyperspaces, Chaos Solitons Fractals, 33 (2007), 76-86.
doi: 10.1016/j.chaos.2005.12.033. |
[17] |
M. Matviichuk, On the dynamics of subcontinua of a tree, J. Difference Equ. Appl., 19 (2013), 223-233.
doi: 10.1080/10236198.2011.634804. |
[18] |
S. B. Nadler, Jr., Continuum Theory: An Introduction, Monographs and Textbooks in Pure and Applied Mathematics, 158, Marcel Dekker, New York, 1992. |
[19] |
A. N. Sharkovsky, Continuous mapping on the limit points of an iteration sequence, (Russian) Ukrain. Mat. Zh., 18 (1966), 127-130. |
[20] |
A. N. Sharkovsky, Partially ordered system of attracting sets, (Russian) Dokl. Akad. Nauk SSSR, 170 (1966), 1276-1278. |
[21] |
M. B. Vereikina and A. N. Sharkovsky, The set of almost-recurrent points of a dynamical system, (Russian. English summary) Dokl. Akad. Nauk Ukrain. SSR Ser. A, 4 (1984), 6-9. |
show all references
References:
[1] |
G. Acosta, A. Illanes and H. Méndez-Lango, The transitivity of induced maps, Topology Appl., 156 (2009), 1013-1033.
doi: 10.1016/j.topol.2008.12.025. |
[2] |
E. Akin, Countable metric spaces and chain transitivity, preprint, 2013. |
[3] |
S. J. Agronsky, A. M. Bruckner, J. G. Ceder and T. L. Pearson, The structure of $\omega$-limit sets for continuous maps,, Real Analysis Exchange, 15 (): 1989.
|
[4] |
A. D. Barwell, C. Good, P. Oprocha and B. E. Raines, Characterizations of $\omega$-limit sets in topologically hyperbolic systems, Discrete Contin. Dyn. Syst., 33 (2013), 1819-1833.
doi: 10.3934/dcds.2013.33.1819. |
[5] |
L. S. Block and W. A. Coppel, Dynamics in One Dimension, Lecture Notes in Mathematics, Vol. 1513, Berlin Heidelberg, Springer-Verlag, 1992. |
[6] |
L. Block and E. Coven, Maps of the interval with every point chain recurrent, Proc. Amer. Math. Soc., 98 (1986), 513-515.
doi: 10.1090/S0002-9939-1986-0857952-8. |
[7] |
L. Block and J. Franke, The chain recurrent set, attractors, and explosions, Ergodic Theory Dynamical Systems, 5 (1985), 321-327.
doi: 10.1017/S0143385700002972. |
[8] |
A. M. Bruckner and J. Smital, The structure of $\omega$-limit sets for continuous maps of the interval, Math. Bohemica, 117 (1992), 42-47. |
[9] |
Y. N. Dowker and F. G. Friedlander, On limit sets in dynamical systems, Proc. London Math. Soc. (3), 4 (1954), 168-176. |
[10] |
V. V. Fedorenko, Asymptotic periodicity of the trajectories of an interval, Ukrainian Math. J., 61 (2009), 854-858.
doi: 10.1007/s11253-009-0238-5. |
[11] |
V. V. Fedorenko, E. Yu. Romanenko and A. N. Sharkovsky, Trajectories of intervals in one-dimensional dynamical systems, J. Difference Equ. Appl., 13 (2007), 821-828.
doi: 10.1080/10236190701396636. |
[12] |
A. Illanes and S. B. Nadler, Jr., Hyperspaces. Fundamentals and Recent Advances, Monographs and Textbooks in Pure and Applied Mathematics, 216, Marcel Dekker, Inc., New York, 1999. |
[13] |
M. Hurley, Chain recurrence and attraction in non-compact spaces, Ergod. Th. & Dynam. Sys., 11 (1991), 709-729.
doi: 10.1017/S014338570000643X. |
[14] |
S. Kolyada and D. Robatian, On omega-limit sets of triangular induced maps, Real Analysis Exchange, 38 (2013), 299-316. |
[15] |
S. Kolyada and L. Snoha, On $\omega$-limit sets of triangular maps,, Real Analysis Exchange, 18 (): 1992.
|
[16] |
D. Kwietniak and P. Oprocha, Topological entropy and chaos for maps induced on hyperspaces, Chaos Solitons Fractals, 33 (2007), 76-86.
doi: 10.1016/j.chaos.2005.12.033. |
[17] |
M. Matviichuk, On the dynamics of subcontinua of a tree, J. Difference Equ. Appl., 19 (2013), 223-233.
doi: 10.1080/10236198.2011.634804. |
[18] |
S. B. Nadler, Jr., Continuum Theory: An Introduction, Monographs and Textbooks in Pure and Applied Mathematics, 158, Marcel Dekker, New York, 1992. |
[19] |
A. N. Sharkovsky, Continuous mapping on the limit points of an iteration sequence, (Russian) Ukrain. Mat. Zh., 18 (1966), 127-130. |
[20] |
A. N. Sharkovsky, Partially ordered system of attracting sets, (Russian) Dokl. Akad. Nauk SSSR, 170 (1966), 1276-1278. |
[21] |
M. B. Vereikina and A. N. Sharkovsky, The set of almost-recurrent points of a dynamical system, (Russian. English summary) Dokl. Akad. Nauk Ukrain. SSR Ser. A, 4 (1984), 6-9. |
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