**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32934

##### New Class of Chaotic Mappings in Symbol Space

**Authors:**
Inese Bula

**Abstract:**

Symbolic dynamics studies dynamical systems on the basis of the symbol sequences obtained for a suitable partition of the state space. This approach exploits the property that system dynamics reduce to a shift operation in symbol space. This shift operator is a chaotic mapping. In this article we show that in the symbol space exist other chaotic mappings.

**Keywords:**
Infinite symbol space,
prefix metric,
chaotic mapping,
generator function,
jump mapping.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1081167

**References:**

[1] M. Azarnoosh, A. M. Nasrabadi, M. R. Mohammadi, M. Firoozabadi, Investigation of mental fatigue through EEG signal processing based on nonlinear analysis: Symbolic dynamics, Chaos, Solitons & Fractals, V.44, 2011, P.10541062.

[2] B. L. Hao, Elementary symbolic dynamics and chaos in dissipative systems, World Scientific, 1989.

[3] B. L. Hao and W. M. Zheng, Applied symbolic dynamics and chaos, Directions in chaos, V.7, World Scientific, 1998.

[4] J. Banks, J. Brooks, G. Cairns, G. Davis and P. Stacey, On Devaney-s definition of chaos, Amer. Math. Monthly, V.99, 1992, P.29-39.

[5] I. Bula and J. Buls, and I. Rumbeniece, Why can we detect the chaos?, Journal of Vibroengineering, V.10, 2008, P.468-474.

[6] I. Bula and J. Buls, and I. Rumbeniece, On chaotic mappings in symbol space, Proceedings of 10th conference on Dynamical Systems ÔÇö Theory and Applications, V.2., P.955-962, Lodz, Poland, 2009.

[7] I. Bula and I. Rumbeniece, Construction of chaotic dynamical system, Mathematical Modelling and Analysis, V.15(1), P.1-8, 2010.

[8] I. Bula, On some chaotic mappings in symbol space Proceedings of the 3rd International Conference on Nonlinear Dynamics, ND-KhPI2010, September 21-24, 2010, Kharkov, Ukraine, P.45-49.

[9] I. Bula and J. Buls, and I. Rumbeniece, On new chaotic mappings in symbol space, Acta Mechanica Sinica (Springer), V.27(1), 2011, P.114- 118.

[10] R. Devaney, An introduction to chaotic dynamical systems, Benjamin Cummings: Menlo Park, CA, 1986.

[11] D. Gulick, Encounters with chaos, McGraw-Hill, Inc., 1992.

[12] B. P. Kitchens, Symbolic Dynamics. One-sided, two-sided and countable state Markov shifts, Springer-Verlag, 1998.

[13] D. Lind D and B. Marcus, An introduction to symbolic dynamics and coding, Cambridge University Press, 1995.

[14] T. Y. Li and J. A. Yorke, Period three implies chaos, Amer. Math. Monthly, V.82(12), 1975, P.985-992.

[15] A. de Luca and S. Varricchio, Finiteness and regularity in semigroups and formal languages, Monographs in Theoretical Computer Science, Springer-Verlag, 1999.

[16] M. Lothaire, Combinatorics on Words, Encyclopedia of Mathematics and its Applications, V.17, Addison-Wesley, Reading, MA, 1983.

[17] M. Morse and G. Hedlund, Symbolic dynamics, Amer. J. Math., V.60, 1938, P.815-866.

[18] C. Robinson, Dynamical systems. Stability, symbolic dynamics, and chaos, CRS Press, 1995.