Author

Igors Gorbovickis

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Preprint Sep 2026

Independence of multipliers via degenerations of rational maps

Using degenerations of rational maps and local asymptotics of periodic multipliers, we prove that for every $d\ge 2$, the multipliers of any $2d-2$ distinct periodic orbits of degree $d$ rational maps are algebraically independent over $\mathbb C$, provided that at most $d$ of the selected orbits are fixed points. This...

Igors Gorbovickis · 0 citations

Preprint Sep 2026

Hyperbolicity of renormalization for maps with multiple breaks

We construct hyperbolic horseshoes for piecewise-analytic homeomorphisms of the circle with {\it multiple} break-type singularities, under the assumptions of bounded type rotation numbers and bounded geometry -- provided the sizes of the breaks are uniformly small. As a consequence, we obtain a $C^{1+\alpha}$-rigidity...

N. Goncharuk, Igors Gorbovickis, Michael Yampolsky · 0 citations