Analogues of Khintchine’s theorem for random attractors
Analogues of Khintchine’s theorem for random attractors
In this paper we study random iterated function systems. Our main result gives sufficient conditions for an analogue of a well known theorem due to Khintchine from Diophantine approximation to hold almost surely for stochastically self-similar and self-affine random iterated function systems.
- University of Birmingham United Kingdom
- University of Vienna Austria
- University of Vienna Austria
- School of Mathematics University of Birmingham United Kingdom
- Universität Wien Austria
101024 Wahrscheinlichkeitstheorie, self-similar systems, Khintchine’s theorem, ABSOLUTE CONTINUITY, Self-affine systems, Dimension theory of smooth dynamical systems, Dynamical Systems (math.DS), Dynamical systems and their relations with probability theory and stochastic processes, self-affine systems, 101025 Number theory, Mathematics - Metric Geometry, Diophantine approximation, Khintchine's theorem, Metric theory, FOS: Mathematics, 101024 Probability theory, Number Theory (math.NT), Mathematics - Dynamical Systems, SETS, 101025 Zahlentheorie, Mathematics - Number Theory, Random iterated function systems, Probability (math.PR), Metric Geometry (math.MG), SELF, Self-similar systems, Random iteration, APPROXIMATION PROPERTIES, FRACTALS, LAWS, Fractals, EXPANSIONS, HAUSDORFF DIMENSION, random iterated function systems, Mathematics - Probability
101024 Wahrscheinlichkeitstheorie, self-similar systems, Khintchine’s theorem, ABSOLUTE CONTINUITY, Self-affine systems, Dimension theory of smooth dynamical systems, Dynamical Systems (math.DS), Dynamical systems and their relations with probability theory and stochastic processes, self-affine systems, 101025 Number theory, Mathematics - Metric Geometry, Diophantine approximation, Khintchine's theorem, Metric theory, FOS: Mathematics, 101024 Probability theory, Number Theory (math.NT), Mathematics - Dynamical Systems, SETS, 101025 Zahlentheorie, Mathematics - Number Theory, Random iterated function systems, Probability (math.PR), Metric Geometry (math.MG), SELF, Self-similar systems, Random iteration, APPROXIMATION PROPERTIES, FRACTALS, LAWS, Fractals, EXPANSIONS, HAUSDORFF DIMENSION, random iterated function systems, Mathematics - Probability
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