Real Analysis Exchange
- Real Anal. Exchange
- Volume 25, Number 1 (1999), 449-462.
Stability Versus Hyperbolicity in Dynamical and Iterated Function Systems
In this paper we investigate a certain notion of stability, for one function or for iterated function systems, and discuss why this notion can be a good extension and complement to the notion of hyperbolicity. This last notion is very well-known in the literature and plays an important role in the investigation of the dynamical behavior of a system. The main result is that although some classical sets of functions like the stable Lipschitz functions are conjugate to hyperbolic functions there exist continuous stable functions which are not conjugate to hyperbolic functions. A sufficient condition for not being conjugate to a hyperbolic function is given.
Real Anal. Exchange, Volume 25, Number 1 (1999), 449-462.
First available in Project Euclid: 5 January 2009
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 26A18: Iteration [See also 37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H25] 26A45: Functions of bounded variation, generalizations 60J05: Discrete-time Markov processes on general state spaces
Ambroladze, Amiran; Markström, Klas; Wallin, Hans. Stability Versus Hyperbolicity in Dynamical and Iterated Function Systems. Real Anal. Exchange 25 (1999), no. 1, 449--462. https://projecteuclid.org/euclid.rae/1231187619