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Wave breaking phenomena and global solutions for a generalized periodic two-component Camassa-Holm system
A Sharkovsky theorem for non-locally connected spaces
1. | Department of Mathematics, Brigham Young University, Provo, UT 84602, United States |
2. | Mathematics Department, Southern Utah University, Cedar City, UT, 84720, United States |
References:
[1] |
Ll. Alsedà, D. Juher and P. Mumbrú, Sets of periods for piecewise monotone tree maps,, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 13 (2003), 311.
doi: 10.1142/S021812740300656X. |
[2] |
Lluís Alsedà, Jaume Llibre and Michał Misiurewicz, Periodic orbits of maps of $Y$,, Trans. Amer. Math. Soc., 313 (1989), 475.
doi: 10.1090/S0002-9947-1989-0958882-0. |
[3] |
Lluís Alsedà, Jaume Llibre and Michał Misiurewicz, "Combinatorial Dynamics and Entropy in Dimension One,'', 2nd edition, 5 (2000).
|
[4] |
Lluís Alsedà i Soler, Periodic points of continuous mappings of the circle,, Publ. Sec. Mat. Univ. Autònoma Barcelona, (1981), 5.
|
[5] |
S. Baldwin, Some limitations toward extending Šarkovskiĭ's theorem to connected linearly ordered spaces,, Houston J. Math., 17 (1991), 39.
|
[6] |
Stewart Baldwin, An extension of Šarkovskiĭ's theorem to the n-od,, Ergodic Theory Dynam. Systems, 11 (1991), 249.
doi: 10.1017/S0143385700006131. |
[7] |
Stewart Baldwin, Versions of Sharkovskiĭ's theorem on trees and dendrites,, Topology Proc., 18 (1993), 19.
|
[8] |
Louis Block, John Guckenheimer, Michał Misiurewicz and Lai Sang Young, Periodic points and topological entropy of one-dimensional maps,, in, 819 (1980), 18.
|
[9] |
Keith Burns and Boris Hasselblatt, The Sharkovsky theorem: A natural direct proof,, Amer. Math. Monthly, 118 (2011), 229.
doi: 10.4169/amer.math.monthly.118.03.229. |
[10] |
A. I. Demin, Coexistence of periodic, almost periodic and recurrent points of transformations of n-od,, Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1996 (1996), 84.
|
[11] |
Robert L. Devaney, "An Introduction to Chaotic Dynamical Systems,'', 2nd edition, (1989).
|
[12] |
Christian Gillot and Jaume Llibre, Periods for maps of the figure-eight space,, Reprint of the paper reviewed in MR1361924 (97d:58161), 8 (1995), 95.
|
[13] |
W. T. Ingram, Periodic points for homeomorphisms of hereditarily decomposable chainable continua,, Proc. Amer. Math. Soc., 107 (1989), 549.
doi: 10.1090/S0002-9939-1989-0984796-1. |
[14] |
Piotr Minc and W. R. R. Transue, Sarkovskiĭ's theorem for hereditarily decomposable chainable continua,, Trans. Amer. Math. Soc., 315 (1989), 173.
doi: 10.2307/2001378. |
[15] |
Michał Misiurewicz, Periodic points of maps of degree one of a circle,, Ergodic Theory Dynamical Systems, 2 (1982), 221.
|
[16] |
Sam B. Nadler, Jr., "Continuum Theory. An Introduction,'', Monographs and Textbooks in Pure and Applied Mathematics, 158 (1992).
|
[17] |
H. Schirmer, A topologist's view of Sharkovsky's theorem,, Houston J. Math., 11 (1985), 385.
|
[18] |
A. N. Sharkovskiĭ, Coexistence of cycles of a continuous map of the line into itself, Translated from the Russian by J. Tolosa,, Proceedings of the Conference, 5 (1995), 1263.
|
[19] |
H. W. Siegberg, Chaotic mappings on $S^1$, periods one, two, three imply chaos on $S^1$,, in, 878 (1981), 351.
|
[20] |
Jin Cheng Xiong, Xiang Dong Ye, Zhi Qiang Zhang and Jun Huang, Some dynamical properties of continuous maps on the Warsaw circle,, (Chinese), 39 (1996), 294.
|
[21] |
Li Zhen Zhou and You Cheng Zhou, Some dynamical properties of continuous self-maps on the $k$-Warsaw circle,, (Chinese), 29 (2002), 12.
|
show all references
References:
[1] |
Ll. Alsedà, D. Juher and P. Mumbrú, Sets of periods for piecewise monotone tree maps,, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 13 (2003), 311.
doi: 10.1142/S021812740300656X. |
[2] |
Lluís Alsedà, Jaume Llibre and Michał Misiurewicz, Periodic orbits of maps of $Y$,, Trans. Amer. Math. Soc., 313 (1989), 475.
doi: 10.1090/S0002-9947-1989-0958882-0. |
[3] |
Lluís Alsedà, Jaume Llibre and Michał Misiurewicz, "Combinatorial Dynamics and Entropy in Dimension One,'', 2nd edition, 5 (2000).
|
[4] |
Lluís Alsedà i Soler, Periodic points of continuous mappings of the circle,, Publ. Sec. Mat. Univ. Autònoma Barcelona, (1981), 5.
|
[5] |
S. Baldwin, Some limitations toward extending Šarkovskiĭ's theorem to connected linearly ordered spaces,, Houston J. Math., 17 (1991), 39.
|
[6] |
Stewart Baldwin, An extension of Šarkovskiĭ's theorem to the n-od,, Ergodic Theory Dynam. Systems, 11 (1991), 249.
doi: 10.1017/S0143385700006131. |
[7] |
Stewart Baldwin, Versions of Sharkovskiĭ's theorem on trees and dendrites,, Topology Proc., 18 (1993), 19.
|
[8] |
Louis Block, John Guckenheimer, Michał Misiurewicz and Lai Sang Young, Periodic points and topological entropy of one-dimensional maps,, in, 819 (1980), 18.
|
[9] |
Keith Burns and Boris Hasselblatt, The Sharkovsky theorem: A natural direct proof,, Amer. Math. Monthly, 118 (2011), 229.
doi: 10.4169/amer.math.monthly.118.03.229. |
[10] |
A. I. Demin, Coexistence of periodic, almost periodic and recurrent points of transformations of n-od,, Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1996 (1996), 84.
|
[11] |
Robert L. Devaney, "An Introduction to Chaotic Dynamical Systems,'', 2nd edition, (1989).
|
[12] |
Christian Gillot and Jaume Llibre, Periods for maps of the figure-eight space,, Reprint of the paper reviewed in MR1361924 (97d:58161), 8 (1995), 95.
|
[13] |
W. T. Ingram, Periodic points for homeomorphisms of hereditarily decomposable chainable continua,, Proc. Amer. Math. Soc., 107 (1989), 549.
doi: 10.1090/S0002-9939-1989-0984796-1. |
[14] |
Piotr Minc and W. R. R. Transue, Sarkovskiĭ's theorem for hereditarily decomposable chainable continua,, Trans. Amer. Math. Soc., 315 (1989), 173.
doi: 10.2307/2001378. |
[15] |
Michał Misiurewicz, Periodic points of maps of degree one of a circle,, Ergodic Theory Dynamical Systems, 2 (1982), 221.
|
[16] |
Sam B. Nadler, Jr., "Continuum Theory. An Introduction,'', Monographs and Textbooks in Pure and Applied Mathematics, 158 (1992).
|
[17] |
H. Schirmer, A topologist's view of Sharkovsky's theorem,, Houston J. Math., 11 (1985), 385.
|
[18] |
A. N. Sharkovskiĭ, Coexistence of cycles of a continuous map of the line into itself, Translated from the Russian by J. Tolosa,, Proceedings of the Conference, 5 (1995), 1263.
|
[19] |
H. W. Siegberg, Chaotic mappings on $S^1$, periods one, two, three imply chaos on $S^1$,, in, 878 (1981), 351.
|
[20] |
Jin Cheng Xiong, Xiang Dong Ye, Zhi Qiang Zhang and Jun Huang, Some dynamical properties of continuous maps on the Warsaw circle,, (Chinese), 39 (1996), 294.
|
[21] |
Li Zhen Zhou and You Cheng Zhou, Some dynamical properties of continuous self-maps on the $k$-Warsaw circle,, (Chinese), 29 (2002), 12.
|
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