Related papers: On the Birkhoff Spectrum for Hyperbolic Dynamics

We prove the Liv\v{s}ic Theorem for arbitrary $GL(m,\mathbb R)$ cocycles. We consider a hyperbolic dynamical system $f : X \to X$ and a H\"older continuous function $A: X \to GL(m,\mathbb R)$. We show that if $A$ has trivial periodic data,…

We prove that a C2 Hamiltonian system H in M is globally hyperbolic if any of the following statements holds: H is robustly topologically stable; H is stably shadowable; H is stably expansive; and H has the stable weak specification…

In this paper we study a class of non-effectively hyperbolic operators vanishing of order 2 on a manifold, on a sub-region of which the spectral structure of the Hamilton map changes type. Suitable normal symplectic coordinates are found…

We prove a Liv\v{s}ic-type theorem for H\"older continuous and matrix-valued cocycles over non-uniformly hyperbolic systems. More precisely, we prove that whenever $(f,\mu)$ is a non-uniformly hyperbolic system and $A:M \to GL(d,\mathbb{R})…

We introduce the notion of a generalized $(C, \lambda)$-structure, which generalizes hyperbolicity to nonlinear dynamics in Banach spaces. The main novelties are that we allow the hyperbolic splitting to be discontinuous, and that in the…

In the case of smooth non-invertible maps which are hyperbolic on folded basic sets $\Lambda$, we give approximations for the Gibbs states (equilibrium measures) of arbitrary H\"{o}lder potentials, with the help of weighted sums of atomic…

Let $f$ be a partially hyperbolic diffeomorphism. $f$ is called has the quasi-shadowing property if for any pseudo orbit $\{x_k\}_{k\in \mathbb{Z}}$, there is a sequence $\{y_k\}_{k\in \mathbb{Z}}$ tracing it in which $y_{k+1}$ lies in the…

A thorough analysis of the general features of $(p=2)$ parasupersymmetric quantum mechanics is presented. It is shown that for both Rubakov--Spiridonov and Beckers--Debergh formulations of $(p=2)$-parasupersymmetric quantum mechanics, the…

A partially hyperbolic diffeomorphism $f$ has quasi-shadowing property if for any pseudo orbit ${x_k}_{k\in \mathbb{Z}}$, there is a sequence of points ${y_k}_{k\in \mathbb{Z}}$ tracing it in which $y_{k+1}$ is obtained from $f(y_k)$ by a…

We prove that the Birkhoff map $\Om$ for KdV constructed on $H^{-1}_0(\T)$ can be interpolated between $H^{-1}_0(\T)$ and $L^2_0(\T)$. In particular, the symplectic phase space $H^{1/2}_0(\T)$ can be described in terms of Birkhoff…

We prove that a domain in the Riemann sphere is Gromov hyperbolic if and only if it is conformally equivalent to a uniform circle domain. This resolves a conjecture of Bonk--Heinonen--Koskela and also verifies Koebe's conjecture…

Let f be a dominant rational map of P^k such that there exists s <k, with lambda_s(f)>lambda_l(f) for all l. Under mild hypotheses, we show that, for A outside a pluripolar set of the group of automorphisms of P^k, the map f o A admits a…

For smooth random dynamical systems we consider the quenched linear and higher-order response of equivariant physical measures to perturbations of the random dynamics. We show that the spectral perturbation theory of Gou\"ezel, Keller, and…

We present a higher-dimensional version of the Poincar\'e-Birkhoff theorem which applies to Poincar\'e time maps of Hamiltonian systems. The maps under consideration are neither required to be close to the identity nor to have a monotone…

Hyperuniform structures are spatial patterns whose fluctuations disappear on long length scales, making them effectively homogeneous when observed from afar. Mathematically, this means that their spectral density, $\tilde{\rho}({\bf k})$,…

In this paper, we study Birkhoff-James orthogonality of bounded linear operators and give a complete characterization of Birkhoff-James orthogonality of bounded linear operators on infinite dimensional real normed linear spaces. As an…

We consider a similar type of scenario for the disappearance of uniform of hyperbolicity as in Bjerkl\"ov and Saprykina (2008, Nonlinearity 21), where it was proved that the minimum distance between invariant stable and unstable bundles has…

We discuss about the denseness of the strong stable and unstable manifolds of partially hyperbolic diffeomorphisms. In this sense, we introduce a concept of m-minimality. More precisely, we say that a partially hyperbolic diffeomorphisms is…

We prove closing lemmas for automorphisms of a Stein manifold with the density property and for endomorphisms of an Oka-Stein manifold. In the former case we need to impose a new tameness condition. It follows that hyperbolic periodic…

We consider the ortho spectrum of hyperbolic surfaces with totally geodesic boundary. We show that in general the ortho spectrum does not determine the systolic length but that there are only finitely many possibilities. As a corollary we…