Hedgehogs of Hausdorff dimension one
Kingshook Biswas
TL;DR
This paper constructs a common hedgehog of Hausdorff dimension one for a family of commuting non-linearisable holomorphic maps with an indifferent fixed point, demonstrating the minimal possible dimension.
Contribution
It introduces a method to construct a common hedgehog of minimal Hausdorff dimension for specific holomorphic maps, advancing understanding of their geometric properties.
Findings
Constructed a common hedgehog of Hausdorff dimension 1
Demonstrated the minimal possible dimension for such structures
Applicable to a family of commuting non-linearisable maps
Abstract
We present a construction of hedgehogs for holomorphic maps with an indifferent fixed point. We construct, for a family of commuting non-linearisable maps, a common hedgehog of Hausdorff dimension 1, the minimum possible.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Holomorphic and Operator Theory