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arXiv · 2602.00293

Smooth Circle Covering with a Physical Measure on a Hyperbolic Repelling Fixed Point

Rubio Gunawan
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Abstract

We construct an example of a smooth ($C^\infty$) circle covering map topologically conjugate to the doubling map, such that it has a physical measure supported on a hyperbolic repelling fixed point. By relaxing the smooth condition at a single point, we also construct an example where the basin of the physical measure has full measure. A key technical step is a realization method of independent interest, which gives a canonical way to construct a full branch map given its induced map.

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Rubio Gunawan. 2026-01-30. Smooth Circle Covering with a Physical Measure on a Hyperbolic Repelling Fixed Point. https://arxiv.org/abs/2602.00293

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