-
Previous Article
Integrability of vector fields versus inverse Jacobian multipliers and normalizers
- DCDS Home
- This Issue
-
Next Article
On a constant rank theorem for nonlinear elliptic PDEs
Mixing invariant extremal distributional chaos
1. | School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China, China, China |
2. | School of Sciences, Dalian Nationalities University, Dalian 116600, China |
References:
[1] |
T. Gedeon, There are no chaotic mappings with residual scrambled sets, Bulletin of the Australian Mathematical Society, 36 (1987), 411-416.
doi: 10.1017/S0004972700003695. |
[2] |
W. Huang and X. D. Ye, Homeomorphisms with the whole compacta being scrambled sets, Ergodic Theory and Dynamical Systems, 21 (2001), 77-91.
doi: 10.1017/S0143385701001079. |
[3] |
T. Y. Li and J. A. Yorke, Period three implies chaos, The American Mathematical Monthly, 82 (1975), 985-992.
doi: 10.2307/2318254. |
[4] |
G .F. Liao, L. D. Wang and X. D. Duan, A chaotic function with a distributively scrambled set of full Lebesgue measure, Nonlinear Analysis: Theory, Methods & Applications, 66 (2007), 2274-2280.
doi: 10.1016/j.na.2006.03.018. |
[5] |
M. Misiurewicz, Chaos almost everywhere, in Iteration Theory and Its Functional Equations, Springer Berlin Heidelberg, 1985.
doi: 10.1007/BFb0076425. |
[6] |
P. Oprocha, Distributional chaos revisited, Transactions of the American Mathematical Society, 361 (2009), 4901-4925.
doi: 10.1090/S0002-9947-09-04810-7. |
[7] |
P. Oprocha, Invariant scrambled sets and distributional chaos, Dynamical Systems, 24 (2009), 31-43.
doi: 10.1080/14689360802415114. |
[8] |
B. Schweitzer and J. Smítal, Measures of chaos and spectral decomposition of dynamical systems of the interval, Transactions of the American Mathematical Society, 344 (1994), 737-754.
doi: 10.1090/S0002-9947-1994-1227094-X. |
[9] |
H. Wang, G. F. Liao and Q. J. Fan, A note on the map with the whole space being a scrambled set, Nonlinear Analysis: Theory, Methods & Applications, 70 (2009), 2400-2402.
doi: 10.1016/j.na.2008.03.024. |
[10] |
H. Wang, F. C. Lei and L. D. Wang, Dense invariant open distributionally scrambled sets and closed distributionally scrambled sets, Topology and its Applications, 165 (2014), 110-120.
doi: 10.1016/j.topol.2014.01.019. |
[11] |
X. Wu and P. Zhu, Invariant scrambled set and maximal distributional chaos, Ann. Polon. Math., 109 (2013), 271-278.
doi: 10.4064/ap109-3-3. |
[12] |
X. Wu, P. Oprocha and G. Chen, On various definitions of shadowing with average error in tracing, Nonlinearity, 29 (2016), 1942-1972. arXiv:1406.5822
doi: 10.1088/0951-7715/29/7/1942. |
show all references
References:
[1] |
T. Gedeon, There are no chaotic mappings with residual scrambled sets, Bulletin of the Australian Mathematical Society, 36 (1987), 411-416.
doi: 10.1017/S0004972700003695. |
[2] |
W. Huang and X. D. Ye, Homeomorphisms with the whole compacta being scrambled sets, Ergodic Theory and Dynamical Systems, 21 (2001), 77-91.
doi: 10.1017/S0143385701001079. |
[3] |
T. Y. Li and J. A. Yorke, Period three implies chaos, The American Mathematical Monthly, 82 (1975), 985-992.
doi: 10.2307/2318254. |
[4] |
G .F. Liao, L. D. Wang and X. D. Duan, A chaotic function with a distributively scrambled set of full Lebesgue measure, Nonlinear Analysis: Theory, Methods & Applications, 66 (2007), 2274-2280.
doi: 10.1016/j.na.2006.03.018. |
[5] |
M. Misiurewicz, Chaos almost everywhere, in Iteration Theory and Its Functional Equations, Springer Berlin Heidelberg, 1985.
doi: 10.1007/BFb0076425. |
[6] |
P. Oprocha, Distributional chaos revisited, Transactions of the American Mathematical Society, 361 (2009), 4901-4925.
doi: 10.1090/S0002-9947-09-04810-7. |
[7] |
P. Oprocha, Invariant scrambled sets and distributional chaos, Dynamical Systems, 24 (2009), 31-43.
doi: 10.1080/14689360802415114. |
[8] |
B. Schweitzer and J. Smítal, Measures of chaos and spectral decomposition of dynamical systems of the interval, Transactions of the American Mathematical Society, 344 (1994), 737-754.
doi: 10.1090/S0002-9947-1994-1227094-X. |
[9] |
H. Wang, G. F. Liao and Q. J. Fan, A note on the map with the whole space being a scrambled set, Nonlinear Analysis: Theory, Methods & Applications, 70 (2009), 2400-2402.
doi: 10.1016/j.na.2008.03.024. |
[10] |
H. Wang, F. C. Lei and L. D. Wang, Dense invariant open distributionally scrambled sets and closed distributionally scrambled sets, Topology and its Applications, 165 (2014), 110-120.
doi: 10.1016/j.topol.2014.01.019. |
[11] |
X. Wu and P. Zhu, Invariant scrambled set and maximal distributional chaos, Ann. Polon. Math., 109 (2013), 271-278.
doi: 10.4064/ap109-3-3. |
[12] |
X. Wu, P. Oprocha and G. Chen, On various definitions of shadowing with average error in tracing, Nonlinearity, 29 (2016), 1942-1972. arXiv:1406.5822
doi: 10.1088/0951-7715/29/7/1942. |
[1] |
Piotr Oprocha. Specification properties and dense distributional chaos. Discrete and Continuous Dynamical Systems, 2007, 17 (4) : 821-833. doi: 10.3934/dcds.2007.17.821 |
[2] |
Piotr Oprocha, Pawel Wilczynski. Distributional chaos via isolating segments. Discrete and Continuous Dynamical Systems - B, 2007, 8 (2) : 347-356. doi: 10.3934/dcdsb.2007.8.347 |
[3] |
Artem Dudko. Computability of the Julia set. Nonrecurrent critical orbits. Discrete and Continuous Dynamical Systems, 2014, 34 (7) : 2751-2778. doi: 10.3934/dcds.2014.34.2751 |
[4] |
Angela A. Albanese, Xavier Barrachina, Elisabetta M. Mangino, Alfredo Peris. Distributional chaos for strongly continuous semigroups of operators. Communications on Pure and Applied Analysis, 2013, 12 (5) : 2069-2082. doi: 10.3934/cpaa.2013.12.2069 |
[5] |
Dominik Kwietniak. Topological entropy and distributional chaos in hereditary shifts with applications to spacing shifts and beta shifts. Discrete and Continuous Dynamical Systems, 2013, 33 (6) : 2451-2467. doi: 10.3934/dcds.2013.33.2451 |
[6] |
Jingna Li, Li Xia. The Fractional Ginzburg-Landau equation with distributional initial data. Communications on Pure and Applied Analysis, 2013, 12 (5) : 2173-2187. doi: 10.3934/cpaa.2013.12.2173 |
[7] |
Marc Briane, Vincenzo Nesi. Distributional convergence of null Lagrangians under very mild conditions. Discrete and Continuous Dynamical Systems - B, 2007, 8 (2) : 493-510. doi: 10.3934/dcdsb.2007.8.493 |
[8] |
Marat Akhmet, Ejaily Milad Alejaily. Abstract similarity, fractals and chaos. Discrete and Continuous Dynamical Systems - B, 2021, 26 (5) : 2479-2497. doi: 10.3934/dcdsb.2020191 |
[9] |
Ryszard Rudnicki. An ergodic theory approach to chaos. Discrete and Continuous Dynamical Systems, 2015, 35 (2) : 757-770. doi: 10.3934/dcds.2015.35.757 |
[10] |
Arsen R. Dzhanoev, Alexander Loskutov, Hongjun Cao, Miguel A.F. Sanjuán. A new mechanism of the chaos suppression. Discrete and Continuous Dynamical Systems - B, 2007, 7 (2) : 275-284. doi: 10.3934/dcdsb.2007.7.275 |
[11] |
Vadim S. Anishchenko, Tatjana E. Vadivasova, Galina I. Strelkova, George A. Okrokvertskhov. Statistical properties of dynamical chaos. Mathematical Biosciences & Engineering, 2004, 1 (1) : 161-184. doi: 10.3934/mbe.2004.1.161 |
[12] |
Y. Charles Li. Chaos phenotypes discovered in fluids. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 1383-1398. doi: 10.3934/dcds.2010.26.1383 |
[13] |
Kaijen Cheng, Kenneth Palmer. Chaos in a model for masting. Discrete and Continuous Dynamical Systems - B, 2015, 20 (7) : 1917-1932. doi: 10.3934/dcdsb.2015.20.1917 |
[14] |
Flaviano Battelli, Michal Fe?kan. Chaos in forced impact systems. Discrete and Continuous Dynamical Systems - S, 2013, 6 (4) : 861-890. doi: 10.3934/dcdss.2013.6.861 |
[15] |
J. Alberto Conejero, Francisco Rodenas, Macarena Trujillo. Chaos for the Hyperbolic Bioheat Equation. Discrete and Continuous Dynamical Systems, 2015, 35 (2) : 653-668. doi: 10.3934/dcds.2015.35.653 |
[16] |
Eric A. Carlen, Maria C. Carvalho, Jonathan Le Roux, Michael Loss, Cédric Villani. Entropy and chaos in the Kac model. Kinetic and Related Models, 2010, 3 (1) : 85-122. doi: 10.3934/krm.2010.3.85 |
[17] |
Lan Wen. On the preperiodic set. Discrete and Continuous Dynamical Systems, 2000, 6 (1) : 237-241. doi: 10.3934/dcds.2000.6.237 |
[18] |
François Berteloot, Tien-Cuong Dinh. The Mandelbrot set is the shadow of a Julia set. Discrete and Continuous Dynamical Systems, 2020, 40 (12) : 6611-6633. doi: 10.3934/dcds.2020262 |
[19] |
Kaijen Cheng, Kenneth Palmer, Yuh-Jenn Wu. Period 3 and chaos for unimodal maps. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 1933-1949. doi: 10.3934/dcds.2014.34.1933 |
[20] |
Jaroslav Smítal, Marta Štefánková. Omega-chaos almost everywhere. Discrete and Continuous Dynamical Systems, 2003, 9 (5) : 1323-1327. doi: 10.3934/dcds.2003.9.1323 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]