Abstract
In this chapter we shall consider one-dimensional mappings which have been intensely studied during the last few years, from the point of view of both dynamical systems and ergodic theory. Phase spaces of these systems are intervals I ⊂ R1 and transformations are real-valued functions determined on I and taking their values in I. We shall study invariant measures of one-dimensional maps, especially absolutely continuous invariant measures. The topological aspect of the problem will be discussed in one of the further volumes.
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© 1989 Springer-Verlag Berlin Heidelberg
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Jakobson, M.V. (1989). Ergodic Theory of One-Dimensional Mappings. In: Sinai, Y.G. (eds) Dynamical Systems II. Encyclopaedia of Mathematical Sciences, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06788-8_9
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DOI: https://doi.org/10.1007/978-3-662-06788-8_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-06790-1
Online ISBN: 978-3-662-06788-8
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