CORDIS Project
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This project investigates the dimensions of stationary fractal measures, focusing on self-affine and self-similar measures. It aims to prove the equality of the measure's dimension with its upper bound using advanced mathematical techniques.
We consider the dimension of stationary fractal measures.
Our examples include self-affine, self-similar, and Furstenberg measures, which are among the most fundamental and studied fractal objects.
The dimension of such a measure has a natural upper bound defined in terms of entropy, Lyapunov exponents, and the dimension of the ambient space.
Equality to the upper bound is expected in the absence of obvious algebraic obstructions.
In very simple situations, this equality is easy to demonstrate a…
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