Abstract: We further develop the thermodynamic formalism of affine iterated function
systems with countably many transformations by showing the existence and extending
earlier characterisations of the equilibrium states of finite affine iterated function
systems to the countably infinite case. As an application, under mild conditions, we
prove that the affinity dimension of a countable affine iterated function system is
equal to the supremum of the affinity dimensions of its finite subsystems. We deduce
corollaries concerning the Hausdorff dimension of countably generated self-affine sets
in dimensions 1, 2, and 3 satisfying mild deterministic assumptions and in arbitrary
dimensions with generic translations. The talk is based on a joint work with Ian Morris.
Thermodynamic formalism of countably generated self-affine sets
22.09.2023 13:15 - 14:15
Organiser:
H. Bruin, R. Zweimüller
Location:
BME Budapest