Abstract
AbstractWe introduce the notion of a strong pair of periodic segments over [0, T] and we show its applications in detecting chaotic dynamics. We prove a various number of fixed point index formulas concerning periodic points of the Poincaré map.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics
Reference21 articles.
1. Conley, C.: Isolated Invariant Sets and the Morse Index, CBMS Regional Conference Series in Mathematics, vol. 38. Amer. Math. Soc, Providence, R.I. (1978)
2. Conley, C., Easton, R.: Isolated invariant sets and isolating blocks. Trans. Amer. Math. Soc. 158, 35–61 (1971)
3. Devaney, R.L.: An Introduction to Chaotic Dynamical Systems. Addison-Wesley, Menlo Park (1985)
4. Dold, A.: Lectures on Algebraic Topology. Springer-Verlag, Berlin (1980)
5. Jezierski, J., Marzantowicz, W.: Homotopy Methods in Topological Fixed and Periodic Point Theory, Springer, (2006)