Bernoulli convolutions and 1D dynamics

Summary, in English

We describe a family phi(lambda) of dynamical systems on the unit interval which preserve Bernoulli convolutions. We show that if there are parameter ranges for which these systems are piecewise convex, then the corresponding Bernoulli convolution will be absolutely continuous with bounded density. We study the systems phi(lambda) and give some numerical evidence to suggest values of lambda for which phi(lambda) may be piecewise convex.

• Författare: Tom Kempton; Tomas Persson
• Avdelning/ar: Matematik LTH; Dynamical systems
• Publiceringsår: 2015
• Språk: Engelska
• Sidor: 3921-3934
• Publikation/Tidskrift/Serie: Nonlinearity
• Volym: 28
• Issue: 11
• Länkar: https://arxiv.org/abs/1501.06740; http://dx.doi.org/10.1088/0951-7715/28/11/3921
• Dokumenttyp: Artikel i tidskrift
• Förlag: London Mathematical Society / IOP Science
• Ämne: Mathematics
• Nyckelord: bernoulli convolutions; tent maps; absolutely continuous invariant; measures
• Status: Published
• Forskningsgrupp: Dynamical systems
• ISBN/ISSN/Övrigt: ISSN: 0951-7715