20.500.12556/DiRROS-27564 Dynamics of skew-products tangent to the identity We study the local dynamics of generic skew-products tangent to the identity, i.e. maps of the form $P(z,w)=(p(z), q(z,w))$ with $dP_0=\mathrm{Id}$. More precisely, we focus on maps with non-degenerate second differential at the origin; such maps have local normal form $P(z,w)=(z-z^2+O(z^3),w+w^2+bz^2+O(\|(z,w)\|^3))$. We prove the existence of parabolic domains, and prove that inside these parabolic domains the orbits converge non-tangentially if and only if $b \in (\frac{1}{4},+\infty)$. Furthermore, we prove the existence of a type of parabolic implosion, in which the renormalization limits are different from previously known cases. This has a number of consequences: under a diophantine condition on coefficients of $P$, we prove the existence of wandering domains with rank $1$ limit maps. We also give explicit examples of quadratic skew-products with countably many grand orbits of wandering domains, and we give an explicit example of a skew-product map with a Fatou component exhibiting historic behaviour. Finally, we construct various topological invariants, which allow us to answer a question of Abate. skew-products germs tangent to identity parabolic implosion wandering domains true false true Angleški jezik Ni določen Neznano 2026-02-13 08:59:33 2026-02-13 08:59:34 2026-02-14 04:04:00 0000-00-00 00:00:00 2026 0 0 str. 559-618 no. 2 Vol. 28 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-01-01 517 1435-9855 10.4171/JEMS/1566 223408643 10.4171-jems-1566.pdf 10.4171-jems-1566.pdf 1 44E0091CAD94C11342B7A72C48200979 45b50cbbf6c141839e2717ee63d7e87eb8e1f5e84a35cb098748a03dfa553049 705f22bb-08b5-11f1-bcbc-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=40381 https://ems.press/journals/jems/articles/14298412 1 f01a67f3-08b1-11f1-bcbc-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=40379 Inštitut za matematiko, fiziko in mehaniko 0 0 0