IJPAM: Volume 86, No. 2 (2013)

ROBUST DENSITY OF PERIODIC SINKS
AND SOURCES FOR ITERATED FUNCTION SYSTEMS

F.H. Ghane1, M. Nazari2, M. Saleh3, Z. Shabani4
1,2,4Department of Mathematics
Ferdowsi University of Mashhad
Mashhad, IRAN
3Department of Mathematics
University of Neyshabur
Neyshabur, IRAN


Abstract. Given any compact m-dimensional manifold M, we describe C1-open sets of iterated function systems admitting infinite number of attracting and repelling periodic orbits. We show that attracting periodic orbits are dense in the ambient manifold M. Also, the same property holds for repelling periodic orbits.

Moreover, the step skew product maps corresponding to these iterated function systems are topologically transitive.

Received: February 18, 2013

AMS Subject Classification: 37E30, 28A20

Key Words and Phrases: iterated function systems, minimal iterated function systems, attracting periodic orbits, repelling periodic orbits

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DOI: 10.12732/ijpam.v86i2.10 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 86
Issue: 2