Alejandro Passeggi
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View article: Conditions Implying Annular Chaos: Quantitative results and Computer Assisted Proofs
Conditions Implying Annular Chaos: Quantitative results and Computer Assisted Proofs Open
We derive quantitative sufficient conditions for rotational chaos and diffusion in annular homeomorphisms, building on the topological criteria established in [31]. These conditions depend only on basic properties of the maps, making their…
View article: A note on weak conjugacy for homeomorphisms of surfaces
A note on weak conjugacy for homeomorphisms of surfaces Open
We explore the relation of weak conjugacy in the group of homeomorphisms isotopic to the identity, for surfaces.
View article: Area preserving homeomorphisms of surfaces with rational rotational direction
Area preserving homeomorphisms of surfaces with rational rotational direction Open
Let $S$ be a closed surface of genus $g\geq 2$, furnished with a Borel probability measure $λ$ with total support. We show that if $f$ is a $λ$-preserving homeomorphism isotopic to the identity such that the rotation vector $\mathrm{rot}_f…
View article: Conditions implying annular chaos
Conditions implying annular chaos Open
This work investigates topological chaos for homeomorphisms of the open annulus, introducing a new set of sufficient conditions based on points with distinct rotation numbers and their topological relation to invariant continua. These cond…
View article: The bifurcation set as a topological invariant for one-dimensional dynamics
The bifurcation set as a topological invariant for one-dimensional dynamics Open
For a continuous map on the unit interval or circle, we define the bifurcation set to be the collection of those interval holes whose surviving set is sensitive to arbitrarily small changes of (some of) their endpoints. By assuming a globa…
View article: Generic Rotation Sets in Hyperbolic Surfaces
Generic Rotation Sets in Hyperbolic Surfaces Open
We show that for generic homeomorphisms homotopic to the identity in a closed and oriented surface of genus $g>1$, the rotation set is given by a union of at most $2^{5g-3}$ convex sets. Examples showing the sharpness for this asymptotic o…
View article: The bifurcation set as a topological invariant for one-dimensional\n dynamics
The bifurcation set as a topological invariant for one-dimensional\n dynamics Open
For a continuous map on the unit interval or circle, we define the\nbifurcation set to be the collection of those interval holes whose surviving\nset is sensitive to arbitrarily small changes of their position. By assuming a\nglobal perspe…
View article: A Poincaré–Bendixson theorem for translation lines and applications to prime ends
A Poincaré–Bendixson theorem for translation lines and applications to prime ends Open
For an orientation-preserving homeomorphism of the sphere, we prove that if a translation line does not accumulate in a fixed point, then it necessarily spirals towards a topological attractor. This is in analogy with the description of fl…
View article: Deviations in the Franks–Misiurewicz conjecture
Deviations in the Franks–Misiurewicz conjecture Open
We show that if there exists a counter example for the rational case of the Franks–Misiurewicz conjecture, then it must exhibit unbounded deviations in the complementary direction of its rotation set.
View article: A Poincar\\'e-Bendixson theorem for translation lines and applications to\n prime ends
A Poincar\\'e-Bendixson theorem for translation lines and applications to\n prime ends Open
For an orientation-preserving homeomorphism of the sphere, we prove that if a\ntranslation line does not accumulate in a fixed point, then it necessarily\nspirals towards a topological attractor. This is in analogy with the\ndescription of…