arXiv subjects

João Carnevale

Publications and source records attributed to João Carnevale.

3 recordsLinked to original sources

arXiv2026

Amalgamated Free Products of Circle Actions with a Bounded Number of Fixed Points

Inspired by constructions of Kovačević, we introduce the amalgamated free product of circle actions, obtained by blowing up two actions along prescribed orbits and rearranging the inserted intervals. Under natural orbit and index assumptions, we prove that this construction is well defined, yields a minimal action on the circle, and is unique up to topological conjugacy. We then study its dynamical properties. Using a proper ping-pong partition arising from the construction, we obtain criteria ensuring that the resulting action still has a uniformly bounded number of fixed points, and in particular at most $2n$ fixed points. We also give sufficient conditions for the resulting action to remain Möbius-like and for it not to be topologically conjugate to a subgroup of any finite lift $\psl^{(k)}(2,\RR)$.

math.DS↗

arXiv2024

Non-locally discrete actions on the circle with at most $N$ fixed points

A subgroup of $\mathrm{Homeo}_+(\mathbb{S}^1)$ is Möbius-like if every element is conjugate to an element of $\mathrm{PSL}(2,\mathbb{R})$. In general, a Möbius-like subgroup of $\mathrm{Homeo}_+(\mathbb{S}^1)$ is not necessarily (semi-)conjugate to a subgroup of $\mathrm{PSL}(2,\mathbb{R})$, as discovered by N. Kovačević [Trans. Amer. Math. Soc. 351 (1999), 4823-4835]. Here we determine simple dynamical criteria for the existence of such a (semi-)conjugacy. We show that Möbius-like subgroups of $\mathrm{Homeo}_+(\mathbb{S}^1)$ which are elementary (namely, preserving a Borel probability measure), are semi-conjugate to subgroups of $\mathrm{PSL}(2,\mathbb{R})$. On the other hand, we provide an example of elementary subgroup of $\mathrm{Diff}^\infty_+(\mathbb{S}^1)$ satisfying that every non-trivial element fixes at most 2 points, which is not isomorphic to any subgroup of $\mathrm{PSL}(2,\mathbb{R})$. Finally, we show that non-elementary, non-locally discrete subgroups acting with at most $N$ fixed points are conjugate to a dense subgroup of some finite central extension of $\mathrm{PSL}(2,\mathbb{R})$.

math.GR↗

arXiv2022

Groups acting on the line with at most $2$ fixed points: an extension of Solodov's theorem

A classical result by Solodov states that if a group acts on the line such that any non-trivial element has at most one fixed point, then the action is either abelian or semi-conjugate to an affine action. We show that the same holds if we relax the assumption, requiring that any non-trivial element has at most 2 fixed points.

math.GR↗