Related papers: Many intermingled basins in dimension 3
It is conjectured that every cusped hyperbolic 3-manifold admits a geometric triangulation, i.e. it is decomposed into positive volume ideal hyperbolic tetrahedra. Here, we show that sufficiently highly twisted knots admit a geometric…
Araujo proved in his thesis \cite{A} that a $C^1$ generic surface diffeomorphism has either infinitely many sinks (i.e. attracting periodic orbits) or finitely many hyperbolic attractors with full Lebesgue measure basin. The goal of this…
In this paper, we classify completely hyperbolic 3-manifolds corresponding to geometric limits of Kleinian surface groups isomorphic to $\pi_1(S)$ for a finite-type hyperbolic surface $S$. In the first of the three main theorems, we…
We discuss various infinite-dimensional configuration spaces that carry measures quasiinvariant under compactly-supported diffeomorphisms of a manifold M corresponding to a physical space. Such measures allow the construction of unitary…
The present paper regards the volume function of a doubly truncated hyperbolic tetrahedron. Starting from the previous results of J. Murakami, U. Yano and A. Ushijima, we have developed a unified approach to express the volume in different…
We consider relativistic hydrodynamics in the limit where the number of spatial dimensions is very large. We show that under certain restrictions, the resulting equations of motion simplify significantly. Holographic theories in a large…
We give a complete topological classification of transitive partially hyperbolic diffeomorphisms in 3-manifolds in terms of Anosov flows, completing a program proposed by Pujals. In particular, this also allows to give a full answer to the…
We construct inhomogenous Markov measures for which the shift is of Kreiger type ${\rm III}_{1}$. These measures are fully supported on a toplogical markov shift space of the hyperbolic toral automorphism…
We study the dynamics of cubic polynomials restricted to their basins of infinity, and we enumerate topological conjugacy classes with given combinatorics.
It is known that sectional-hyperbolic attracting sets, for a $C^2$ flow on a finite dimensional compact manifold, have at most finitely many ergodic physical invariant probability measures. We prove an upper bound for the number of distinct…
We determine topological properties of Stein domains with boundary diffeomorphic to T^3, S^1\times S^2 and some Seifert fibered 3-manifolds.
We study $C^1$-robustly transitive and nonhyperbolic diffeomorphisms having a partially hyperbolic splitting with one-dimensional central bundle whose strong un-/stable foliations are both minimal. {In dimension $3$, an important class of…
The aim of this work is to study a kind of refinement of the entropy conjecture, in the context of partially hyperbolic diffeomorphisms with one dimensional central direction, of d-dimensional torus. We start by establishing a connection…
In this paper we construct some "pathological" volume preserving partially hyperbolic diffeomorphisms on $\toro{3}$ such that their behaviour in small scales in the central direction (Lyapunov exponent) is opposite to the behavior of their…
Every partially hyperbolic diffeomorphism on a 3-dimensional nilmanifold is leaf conjugate to a nilmanifold automorphism.
We constructed a DA on $\mathbb{T}^3$, which complements the work of Gan, Li, Viana, and Yang (\cite{GanLiVianaYang2021}) by providing an example of a $C^\infty$-diffeomorphism with partial volume expansion, where $\dim(E^{cs}) = 2$. In…
We consider Hamiltonian diffeomorphisms of the Euclidean space, generated by compactly supported time-dependent perturbations of hyperbolic quadratic forms. We prove that, under some natural assumptions, such a diffeomorphism must have…
We construct examples of closed non-Haken hyperbolic 3-manifolds with a Heegaard splitting of arbitrarily large distance.
We consider partially hyperbolic diffeomorphisms on compact manifolds where the unstable and stable foliations stably carry some unique non-trivial homologies. We prove the following two results: if the center foliation is one dimensional,…
In this paper, we show that Gromov-Thurston's principle works for hyperbolic 3-manifolds of infinite volume and with finitely generated fundamental group. As an application, we have a new proof of Ending Lamination Theorem. Our proof…