Topological Dynamics in Tandem with Permutation Groups

Author(s)
Isaac Kwame Dontwi^{*},
William Obeng-Denteh^{*},
Stephen K. Manu^{*},
Richard Nyarko Yeboah^{*}

Affiliation(s)

Department of Mathematics, College of Science, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.

Department of Mathematics, College of Science, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.

ABSTRACT

The purpose of this study was to delve into the aspects of abstract algebra that has a link with topological dynamics in terms of permutation and symmetric groups. This would aid users to appreciate the role it plays in the theory and application of topological dynamics. The usage of matlab programming to carry out the permutations was carried out. The study contributes to the literature by providing candid explanation and usage of data-based evidence documenting the extent to which topological dynamics operates.

Cite this paper

I. Dontwi, W. Obeng-Denteh, S. Manu and R. Yeboah, "Topological Dynamics in Tandem with Permutation Groups,"*Advances in Pure Mathematics*, Vol. 3 No. 2, 2013, pp. 292-296. doi: 10.4236/apm.2013.32041.

I. Dontwi, W. Obeng-Denteh, S. Manu and R. Yeboah, "Topological Dynamics in Tandem with Permutation Groups,"

References

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[23] J. Bichon, “Algebraic Quantum Permutation Groups,” Asian European Journal of Mathematics, 2006. http://Arxiv.Org/Abs/0710.1521

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[26] G. R. Sell, “Topological Dynamics and Ordinary Differential Equations,” Van Nostrand-Reinhold Company, London, 1971.

[27] W. H. Gottschalk, “Minimal Sets: An Introduction to Topological Dynamics,” Bulletin of the American Mathematical Society, Vol. 64, 1958, pp. 336-351. doi:10.1090/S0002-9904-1958-10223-2

[28] J. B. Fraleigh, “A First Course in Abstract Algebra,” Pearson Education Inc., Boston, 2003.

[29] W. Obeng-Denteh, “On the Study of Topological Dynamical Systems,” PhD Thesis Draft, Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, 2012.

[1] E. Glasner and B. Weiss, “On the Interplay between Measurable and Topological Dynamics,” Most, Vol. 1, 2004, pp. 1-47.

[2] A. Katok and B. Hasselblatt, “Introduction to the Modern Theory of Dynamical Systems,” October, Cambridge University Press, Cambridge, Vol. 54, 1995, pp. 519-522. doi:10.1017/CBO9780511809187.018

[3] J. P. Boon and O. Decroly, “Dynamical Systems Theory for Music Dynamics,” Chaos, Vol. 5, No. 3, 1994, pp. 501-508. doi:10.1063/1.166145

[4] E. Ball, “Qualitative Research,” Palgrave Macmillan, London, Vol. 5, 2011, pp. 285-306

[5] N. Kruse, “Global Asymptotic Stability in Some Discrete Dynamical Systems,” Journal of Mathematical Analysis and Applications, Vol. 235, No. 1, 1999, pp. 151-158. doi:10.1006/jmaa.1999.6384

[6] N. Chernov, “On Some Statistical Properties of Dynamical Systems,” Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, Vol. 3, 2008, pp. 315-320.

[7] R. Markarian, “Statistical Properties of Dynamical Systems with Singularities,” Journal of Statistical Physics, Vol. 80, No. 5-6, 1995, pp. 1207-1239. doi:10.1007/BF02179869

[8] W. Mitkowski, “Scaling Properties of Discrete Dynamical Systems,” Bulletin of the Polish Academy of Sciences Technical Sciences, Vol. 56, No. 4, 2008.

[9] R. A. Johnson, K. J. Palmerand and G. R. Sell, “Ergodic Properties of Linear Dynamical Systems,” SIAM Journal on Mathematical Analysis, Vol. 18, No. 2, 1987, pp. 191-202. doi:10.1137/0518001

[10] J. M. Mφller, “General Topology,” Topology, 2009, pp. 1-70.

[11] B. Audoly, “Asymptotic Study of the Interfacial Crack with Friction,” Journal of the Mechanics and Physics of Solids, Vol. 48, No. 9, 2000, pp. 1851-1864. doi:10.1016/S0022-5096(99)00098-8

[12] K. Hellan, “An Asymptotic Study of Slow Radial Cracking,” International Journal of Fracture, Vol. 26, No. 1, 1984, pp. 17-30. doi:10.1007/BF01152309

[13] C. Song, H. Gao and X. W. Zheng, “A Study of Asymptotic Stability for Delayed Recurrent Neural Networks,” IEEE International Symposium on Circuits and Systems, Taipei, 24-27 May 2009, pp. 2125-2128.

[14] L. Beiraodaveiga, “Asymptotic Study of the Solution for Pinched Cylindrical Shells,” Computer Methods in Applied Mechanics and Engineering, Vol. 194, No. 9-11, 2005, pp. 1113-1139. doi:10.1016/j.cma.2004.06.015

[15] J. L. Kelley, “General Topology,” Van Nostrand, Princeton, 1955.

[16] C. Othmer, “A Continuous Adjoint Formulation for the Computation of Topological and Surface Sensitivities of Ducted Flows,” Topology, Vol. 58, 2008, pp. 861-877.

[17] D. G. Davis, “Continuous Action,” Journal of Pure and Applied Algebra, Vol. 206, 2006, pp. 322-354. doi:10.1016/j.jpaa.2005.06.022

[18] D. Repovs and L. Zdomskyy, “A New Lindelof Topological Group,” Topology and Its Applications, Vol. 157, No. 5, 2010, pp. 1-8.

[19] O. Pavlov, “A First Countable Linearly Lindelof Not Lindelof Topological Space,” Topology and Its Applications, Vol. 1, 2005, pp. 1-9.

[20] C. Adams and R. Franzoza, “Introduction to Topology: Pure and Applied,” Pearson Prentice Hall, 2008.

[21] P. J. Cameron, “Permutation Groups,” In R. L. Graham, M. Grotschel and L. Lovasz, Eds., Handbook of Combinatorics, Elsevier and the MIT Press, Vol. 1, 1995.

[22] S. Shelah and S. Thomas, “Homogeneity of Infinite Permutation Groups,” Archive for Mathematical Logic, Vol. 28, No. 2, 1989, pp. 143-147. doi:10.1007/BF01633987

[23] J. Bichon, “Algebraic Quantum Permutation Groups,” Asian European Journal of Mathematics, 2006. http://Arxiv.Org/Abs/0710.1521

[24] J. Renshaw, “Inverse Semigroups Acting On Graphs,” World Scientific, 2010. http://www.worldscibooks.com/Mathematics/5584.html

[25] V. Katz, “Historical Notes,” In: J. B. Fraleigh, A First Course in Abstract Algebra, Pearson Education Inc., Boston, 2003.

[26] G. R. Sell, “Topological Dynamics and Ordinary Differential Equations,” Van Nostrand-Reinhold Company, London, 1971.

[27] W. H. Gottschalk, “Minimal Sets: An Introduction to Topological Dynamics,” Bulletin of the American Mathematical Society, Vol. 64, 1958, pp. 336-351. doi:10.1090/S0002-9904-1958-10223-2

[28] J. B. Fraleigh, “A First Course in Abstract Algebra,” Pearson Education Inc., Boston, 2003.

[29] W. Obeng-Denteh, “On the Study of Topological Dynamical Systems,” PhD Thesis Draft, Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, 2012.