| Type of Material: | Thesis |
| Title: | Some combinatorial results in topological dynamics |
| Researcher: | Subramania, Pillai I |
| Guide: | Tandon, R | Raghavendra Rao, C |
| Department: | Department of Mathematics and Statistics |
| Publisher: | University of Hyderabad, Hyderabad |
| Place: | Hyderabad |
| Year: | March 2010 |
| Language: | English |
| Subject: | Mathematics | Statistics | Topological Dynamics | Green ordering | discrete dynamical system | Physical and Basic Sciences |
| Dissertation/Thesis Note: | PhD |
| Fulltext: | Shodhganga |
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| 035 | __ | |a(IN-AhILN)th_447288 |
| 040 | __ | |aHYDR_500046|dIN-AhILN |
| 041 | __ | |aeng |
| 100 | __ | |aSubramania, Pillai I|eResearcher |
| 110 | __ | |aDepartment of Mathematics and Statistics|bUniversity of Hyderabad, Hyderabad|dHyderabad|ein |
| 245 | __ | |aSome combinatorial results in topological dynamics |
| 260 | __ | |aHyderabad|bUniversity of Hyderabad, Hyderabad|cMarch 2010 |
| 300 | __ | |aviii, 100p.|c-|dNone |
| 500 | __ | |aAppendix 97p., Bibliography p.98-100 |
| 502 | __ | |bPhD |
| 518 | __ | |oDate of Award|d 2010 |
| 518 | __ | |oDate of Registration|d August 2008 |
| 520 | __ | |aThe main results of this thesis are combinatorial in nature. We will be mainly working with the continuous automorphisms on the torus T2 and with the continuous self maps on R. The thesis is conveniently divided into _ve chapters. The general mathematical setting is that of an abstract dynamical system with discrete time parameter, that is, a pair (X; f) where X is a topological space and f a continuous mapping of X into itself. We are interested in the action of the iterates of f on X.Chapter-1 is introductory in nature. We explain the basic notions of discrete dynamical systems and some important results emphasizing the role of the set of periodic points and the set of periods in chaos. We discuss briey about the de_nitions of chaos due to Devaney and Li-Yorke. It is already known [21] that for a hyperbolic (having no eigen values on the unit circle) continuous toral automorphism, the periodic points are precisely the rational points. In chapter-2, we calculate the set of periodic points for other continu |
| 650 | __ | |aPhysical and Basic Sciences|2AIU |
| 653 | __ | |aMathematics |
| 653 | __ | |aStatistics |
| 653 | __ | |aTopological Dynamics |
| 653 | __ | |aGreen ordering |
| 653 | __ | |adiscrete dynamical system |
| 700 | __ | |aTandon, R|eGuide |
| 700 | __ | |aRaghavendra Rao, C|eGuide |
| 856 | __ | |uhttp://shodhganga.inflibnet.ac.in/handle/10603/4165|yShodhganga |
| 905 | __ | |afromsg |
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