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Distribution of random orbits according to an IFS

Grant number: 22/10341-9
Support Opportunities:Scholarships in Brazil - Post-Doctorate
Effective date (Start): September 01, 2022
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Ali Tahzibi
Grantee:Graccyela Rosybell Salcedo Pirela
Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Associated research grant:17/06463-3 - Probabilistic and algebraic aspects of smooth dynamical systems, AP.TEM


As with any dynamical system, we are interested in knowing the asymptotic behavior of individual orbits. Our objective is to describe and classify the distribution of random orbits with respect to an IFS. By fixing an interesting distribution (eg Gibss measure) at the base, we want to establish a principle of invariance for IFSs. The idea is to consider a distribution in the base different from Bernoulli, that is, that the process of choosing maps at each time is not independent and equally distributed. In case we have this Invariance Principle, we could establish the existence and uniqueness of the stationary measure, which would imply stability in the distribution of random orbits. (AU)

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