Related papers: On the hyperbolicity of the Feigenbaum fixed point

We single out a notion of staticity which applies to any domain in hyperbolic space whose boundary is a non-compact totally umbilical hypersurface. For (time-symmetric) initial data sets modeled at infinity on any of these latter examples,…

We consider fixed points of the Feigenbaum (periodic-doubling) operator whose orders tend to infinity. It is known that the hyperbolic dimension of their Julia sets go to 2. We prove that the Lebesgue measure of these Julia sets tend to…

We study the angular derivative problem for petals of one-parameter semigroups of holomorphic self-maps of the unit disk. For hyperbolic petals we prove a necessary and sufficient condition for the conformality of the petal in terms of the…

We prove results related to robust transitivity and density of periodic points of Partially Hyperbolic Diffeomorphisms under conditions involving Accessibility and a property in the tangent bundle .

We define the infinite dimensional simplex to be the closure of the convex hull of the standard basis vectors in R^infinity, and prove that this space has the 'fixed point property': any continuous function from the space into itself has a…

We prove a combination theorem for trees of (strongly) relatively hyperbolic spaces and finite graphs of (strongly) relatively hyperbolic groups. This gives a geometric extension of Bestvina and Feighn's Combination Theorem for hyperbolic…

We explicitly show that symmetric Frobenius structures on a finite-dimensional, semi-simple algebra stand in bijection to homotopy fixed points of the trivial SO(2)-action on the bicategory of finite-dimensional, semi-simple algebras,…

In this paper we study the existence and regularity of stable manifolds associated to fixed points of parabolic type in the differentiable and analytic cases, using the parametrization method. The parametrization method relies on a suitable…

We prove a fixed point theorem for closed-graphed, decomposable-valued correspondences whose domain and range is a decomposable set of functions from an atomless measure space to a topological space. One consequence is an improvement of the…

Let $n$ be a positive integer and let $\mathbb F_{q^n}$ be the finite field with $q^n$ elements, where $q$ is a power of a prime. This paper introduces a natural action of the Projective Semilinear Group $\text{P}\Gamma \text{L}(2,…

Let $(f_\lambda)_{\lambda\in \Lambda}$ be a holomorphic family of polynomial automorphisms of $\mathbb{C}^2$. Following previous work of Dujardin and Lyubich, we say that such a family is weakly stable if saddle periodic orbits do not…

We study shadowing property for a partially hyperbolic diffeomorphism $f$. It is proved that if $f$ is dynamically coherent then any pseudotrajectory can be shadowed by a pseudotrajectory with "jumps" along the central foliation. The proof…

This article focus on the connected locus of the cubic polynomial slice $Per_1(\lambda)$ with a parabolic fixed point of multiplier $\lambda=e^{2\pi i\frac{p}{q}}$. We first show that any parabolic component, which is a parallel notion of…

We show that, on a closed semipositive symplectic manifold with semisimple quantum homology, any Hamiltonian diffeomorphism possessing more contractible fixed points, counted homologically, than the total Betti number of the manifold, must…

For a finite and positive measure space $(\Omega,\Sigma,\mu)$ and any weakly compact convex subset of $L\sp\infty(\Omega,\Sigma,mu)$, a fixed point theorem for a class of nonexpansive self-mappings is proved. An analogous result is obtained…

We study fixed point sets for holomorphic automorphisms (and endomorphisms) on complex manifolds. The main object of our interest is to determine the number and configuration of fixed points that forces an automorphism (endomorphism) to be…

We study the Lefschetz fixed point formula for constructible sheaves with higher-dimensional fixed point sets. We give another proof to the explicit description of Lefschetz cycles in our previous paper. For this purpose, we introduce a new…

Let $\Delta$ be a simply connected domain and $f:\mathbb{D} \to \Delta$, where $\mathbb{D}$ is the unit disk, be a corresponding Riemann map. Let ${z_n}\subset \Delta$ be a sequence with no accumulation points inside $\Delta$. In the…

For geometric Lorenz attractors (including the classical Lorenz attractor) we obtain a greatly simplified proof of the central limit theorem which applies also to the more general class of codimension two singular hyperbolic attractors. We…

In this paper we consider semilinear equations $-\Delta u=f(u)$ with Dirichlet boundary conditions on certain convex domains of the two dimensional model spaces of constant curvature. We prove that a positive, semi-stable solution $u$ has…