Related papers: A variational principle for systems with nonunifor…
It is widely known that when $X$ is compact Hausdorff, and when $T: X \to X$ and $f: X \to \mathbb{R}$ are continuous, \begin{equation*} P(T,f) = \sup_{\text{$\mu$: Radon probability}} \left( h_\mu(T) + \int f\, \mathrm{d}\mu \right),…
We demonstrate that hyperuniformity, the suppression of density fluctuations at large length scales, emerges generically from the interplay between conservation laws and non-equilibrium driving. The underlying mechanism for this emergence…
We show that the stable and unstable sets of non-uniformly hyperbolic horseshoes arising in some heteroclinic bifurcations of surface diffeomorphisms have the value conjectured in a previous work by the second and third authors of the…
We conduct the multifractal analysis of the level sets of the asymptotic behavior of almost-additive continuous potentials $(\phi_n)_{n=1}^\infty$ on a topologically mixing subshift of finite type $X$ endowed itself with a metric associated…
We prove three formulas for computing topological pressure of $C^1$-generic conservative diffeomorphism and show the continuity of topological pressure with respect to these diffeomorphisms. We prove for these generic diffeomorphisms that…
We develop the nonuniformly hyperbolic theory for $C^1$ diffeomorphisms admitting continuous invariant splitting without domination. This framework includes stable manifold theorems, shadowing and closing lemmas, the existence of horseshoes…
Without any additional conditions on subadditive potentials, this paper defines subadditive measure-theoretic pressure, and shows that the subadditive measure-theoretic pressure for ergodic measures can be described in terms of…
Recently Lewis Bowen introduced a notion of entropy for measure-preserving actions of a countable sofic group on a standard probability space admitting a generating partition with finite entropy. By applying an operator algebra perspective…
Although it is well known that the Ward identities prohibit anomalous dimensions for conserved currents in local field theories, a claim from certain holographic models involving bulk dilaton couplings is that the gauge field associated…
Let $D$ be an indefinite quaternion division algebra over $\mathbb{Q}$. We approach the problem of bounding the sup-norms of automorphic forms $\phi$ on $D^\times(\mathbb{A})$ that belong to irreducible automorphic representations and…
We prove a Caffarelli--Kohn--Nirenberg inequality in the hyperbolic space. For a semilinear elliptic equation involving the associated weighted Laplace--Beltrami operator, we establish variationally the existence of positive radial…
In this paper, we define and study unstable measure theoretic pressure for C^1-smooth partially hyperbolic diffeomorphisms with sub-additive potentials. For any ergodic measure, we show that this unstable metric pressure equals the…
Variational principles for magnetohydrodynamics (MHD) were introduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of…
It is argued that, for strongly non-linear behaviors, a fully deterministic position can hardly be maintained in the micro-macro transitions. This is due to the lack of information on the relevant boundary conditions, and to the tendency of…
Recent years have seen the development of a rich phenomenology beyond the Luttinger Liquid model of one dimensional quantum fluids, arising from interactions between the elementary phonon excitations. It has been known for some time,…
We study the ergodic theory of non-conservative C^1-generic diffeomorphisms. First, we show that homoclinic classes of arbitrary diffeomorphisms exhibit ergodic measures whose supports coincide with the homoclinic class. Second, we show…
We discuss selected topics of current research interest in the theory of dynamical systems, with emphasis on dimension theory, multifractal analysis, and quantitative recurrence. The topics include the quantitative versus the qualitative…
We prove robustness and uniqueness of equilibrium states for a class of partially hyperbolic diffeomorphisms with dominated splittings and H\"older continuous potentials with not very large oscillation.
We here establish the higher fractional differentiability for solutions to a class of obstacle problems with non-standard growth conditions. We deal with the case in which the solutions to the obstacle problems satisfy a variational…
Let $f: M \to M$ be a $C^r$-diffeomorphism, $r\geq 1$, defined on a compact boundaryless $d$-dimensional manifold $M$, $d\geq 2$, and let $H(p)$ be the homoclinic class associated to the hyperbolic periodic point $p$. We prove that if there…