Related papers: Robust Transitivity for Endomorphisms

We show that for a convex solid set of positive random variables to be tight, or equivalently bounded in probability, it is necessary and sufficient that it is radially bounded, i.e. that every ray passing through one of its elements…

In this paper we give a necessary and sufficient condition for local controllability around closed orbits for general smooth control systems. We also prove that any such system on a compact manifold has a closed orbit.

Let f be a non-invertible holomorphic endomorphism of P^k having an attracting set A. We show that, under some natural assumptions, A supports a unique invariant positive closed current \tau, of the right bidegree and of mass 1. Moreover,…

Let $S$ be a finitely generated abelian semigroup of invertible linear operators on a finite dimensional real or complex vector space $V$. We show that every coarsely dense orbit of $S$ is actually dense in $V$. More generally, if the orbit…

We examine the justification for taking the Event Horizon Telescope's famous 2019 image to be a reliable representation of the region surrounding a black hole. We argue that it takes the form of a robustness argument, with the resulting…

We analyze the robustness of topological order in the toric code in an open boundary setting in the presence of perturbations. The boundary conditions are introduced on a cylinder, and are classified into condensing and non-condensing…

This paper derives a differential contraction condition for the existence of an orbitally-stable limit cycle in an autonomous system. This transverse contraction condition can be represented as a pointwise linear matrix inequality (LMI),…

We present a necessary and sufficient condition for a finite dimensional density matrix to be an extreme point of the convex set of density matrices with positive partial transpose with respect to a subsystem. We also give an algorithm for…

Let $f$ be a $C^2$ partially hyperbolic diffeomorphisms of ${\mathbb T}^3$ (not necessarily volume preserving or transitive) isotopic to a linear Anosov diffeomorphism $A$ with eigenvalues $$\lambda_{s}<1<\lambda_{c}<\lambda_{u}.$$ Under…

We present a definable smooth version of the Thom transversality theorem. We show further that the set of non-transverse definable smooth maps is nowhere dense in the definable smooth topology. Finally, we prove a definable version of a…

We give both sufficient conditions and necessary conditions for the stochastic stability of non-uniformly expanding maps either with or without critical sets. We also show that the number of probability measures describing the statistical…

The theoretical and numerical understanding of the key concept of topological entropy is an important problem in dynamical systems. Most studies have been carried out on maps (discrete-time systems). We analyse a scenario of global changes…

A homeomorphism on a compact metric space is said hyper-expansive if every pair of different compact sets are separated by the homeomorphism in the Hausdorff metric. We characterize such dynamics as those with a finite number of orbits and…

For several decades now it has been known that systems with shearless invariant tori, nontwist Hamiltonian systems, possess barriers to chaotic transport. These barriers are resilient to breakage under perturbation and therefore regions…

Various processes can induce long-lived overdense rings and arcs in protoplanetary and AGN accretion discs, such as the accumulation of gas at the outer edge of the dead zone, or the infall of material. Using the local approximation of…

We consider an effective action of a compact (n-1)-torus on a smooth 2n-manifold with isolated fixed points. We prove that under certain conditions the orbit space is a closed topological manifold. In particular, this holds for certain…

We prove that sectional-hyperbolic attracting sets for $C^1$ vector fields are robustly expansive (under an open technical condition of strong dissipative for higher codimensional cases). This extends known results of expansiveness for…

In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…

We consider the classical problem of the continuation of periodic orbits surviving to the breaking of invariant lower dimensional resonant tori in nearly integrable Hamiltonian systems. In particular we extend our previous results…

We prove that biholomorphisms between the transport twistor spaces of simple or Anosov surfaces exhibit rigidity: they must be, up to constant rescaling and the antipodal map, the lift of an orientation preserving isometry.