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- W3046152545 abstract "This is the second part of our study of the dimension theory of $C^1$ iterated function systems (IFSs) and repellers on ${Bbb R}^d$. In the first part we proved that the upper box-counting dimension of the attractor of any $C^1$ IFS on ${Bbb R}^d$ is bounded above by its singularity dimension, and the upper packing dimension of any ergodic invariant measure associated with this IFS is bounded above by its Lyapunov dimension. Here we introduce a generalized transversality condition (GTC) for parametrized families of $C^1$ IFSs, and show that these upper bounds give actually the dimensions for ``typical'' $C^1$ IFSs under this transversality condition. Moreover we verify the GTC for some parametrized families of $C^1$ IFSs on ${Bbb R}^d$." @default.
- W3046152545 created "2020-08-03" @default.
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- W3046152545 date "2021-06-28" @default.
- W3046152545 modified "2023-09-23" @default.
- W3046152545 title "Dimension estimates for $C^1$ iterated function systems and repellers. Part II" @default.
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