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math.DS2004★ 3 cited
Markov Extensions and Conditionally Invariant Measures for Certain Logistic Maps with Small Holes
Mark F. Demers
We study the family of quadratic maps f_a(x) = 1 - ax^2 on the interval [-1,1] with a between 0 and 2. When small holes are introduced into the system, we prove the existence of an…
math.DS2004
Markov Extensions for Dynamical Systems with Holes: An Application to Expanding Maps of the Interval
Mark Demers
We introduce the Markov extension, represented schematically as a tower, to the study of dynamical systems with holes. For tower maps with small holes, we prove the existence of co…