On the Set of Fixed Points and Periodic Points of Continuously Differentiable Functions

On the Set of Fixed Points and Periodic Points of Continuously Differentiable Functions

In recent years, researchers have studied the size of different sets related to the dynamics of self-maps of an interval. In this note we investigate the sets of fixed points and periodic points of continuously differentiable functions and show that typically such functions have a finite set of fixe...

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Bibliographic Details
Main Author: Aliasghar Alikhani-Koopaei
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2013/929475
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spelling doaj-6c1f9765ae5f4cd7bd065c37a15474a12020-11-25T00:09:00ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252013-01-01201310.1155/2013/929475929475On the Set of Fixed Points and Periodic Points of Continuously Differentiable FunctionsAliasghar Alikhani-Koopaei0Department of Mathematics, Berks College, Pennsylvania State University, Tulpehocken Road, P.O. Box 7009, Reading, PA 19610-6009, USAIn recent years, researchers have studied the size of different sets related to the dynamics of self-maps of an interval. In this note we investigate the sets of fixed points and periodic points of continuously differentiable functions and show that typically such functions have a finite set of fixed points and a countable set of periodic points.http://dx.doi.org/10.1155/2013/929475
collection DOAJ
language English
format Article
sources DOAJ
author Aliasghar Alikhani-Koopaei
spellingShingle Aliasghar Alikhani-Koopaei
On the Set of Fixed Points and Periodic Points of Continuously Differentiable Functions
International Journal of Mathematics and Mathematical Sciences
author_facet Aliasghar Alikhani-Koopaei
author_sort Aliasghar Alikhani-Koopaei
title On the Set of Fixed Points and Periodic Points of Continuously Differentiable Functions
title_short On the Set of Fixed Points and Periodic Points of Continuously Differentiable Functions
title_full On the Set of Fixed Points and Periodic Points of Continuously Differentiable Functions
title_fullStr On the Set of Fixed Points and Periodic Points of Continuously Differentiable Functions
title_full_unstemmed On the Set of Fixed Points and Periodic Points of Continuously Differentiable Functions
title_sort on the set of fixed points and periodic points of continuously differentiable functions
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2013-01-01
description In recent years, researchers have studied the size of different sets related to the dynamics of self-maps of an interval. In this note we investigate the sets of fixed points and periodic points of continuously differentiable functions and show that typically such functions have a finite set of fixed points and a countable set of periodic points.
url http://dx.doi.org/10.1155/2013/929475
work_keys_str_mv AT aliasgharalikhanikoopaei onthesetoffixedpointsandperiodicpointsofcontinuouslydifferentiablefunctions
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