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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:62474", author = "Inese Bula", title = "New Class of Chaotic Mappings in Symbol Space", 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.", volume = "6", number = "7", pages = "775-5", }
