Nonisolated slow convergence in discrete dynamical systems. (English) Zbl 1059.37027
Summary: We introduce a new concept of time convergence that measures the nonisolated slowness of convergence of orbits for discrete dynamical systems. This concept permits us to classify the behavior of complicated slower discrete dynamical systems. We illustrate this fact with nontrivial examples.
MSC:
| 37E05 | Dynamical systems involving maps of the interval |
| 39A12 | Discrete version of topics in analysis |
| 37G99 | Local and nonlocal bifurcation theory for dynamical systems |
References:
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| [2] | Bai-Lin, H.; Zheng, W.-M, Applied Symbolic Dynamics and Chaos (1998), World Scientific: World Scientific Singapore · Zbl 0914.58017 |
| [3] | Solis, F.; Felipe, R., Slow convergence of maps, Journal of Nonlinear Studies, 8, 3, 389-392 (2001) · Zbl 1004.39501 |
| [4] | Feigenbaum, M., Quantitative universality for a class of nonlinear transformations, Journal of Statistical Physics, 19, 1, 25-52 (1978) · Zbl 0509.58037 |
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