Related papers: Gibbs-Markov-Young structures with (stretched) exp…
For perturbations of integrable Hamiltonians systems, the Nekhoroshev theorem shows that all solutions are stable for an exponentially long interval of time, provided the integrable part satisfies a steepness condition and the system is…
We prove that the set of fiber-bunched $SL(2,\mathbb{R})$-valued H\"{o}lder cocycles with nonvanishing Lyapunov exponents over a volume preserving, accessible and center-bunched partially hyperbolic diffeomorphism is open. Moreover, we…
We introduce a novel approach linking fractal geometry to partially hyperbolic dynamics, revealing several new phenomena related to regularity jumps and rigidity. One key result demonstrates a sharp phase transition for partially hyperbolic…
We show that diffeomorphisms with a dominated splitting of the form $E^s\oplus E^c\oplus E^u$, where $E^c$ is a nonhyperbolic central bundle that splits in a dominated way into 1-dimensional subbundles, are entropy-expansive. In particular,…
Using a multi-scaled, chaotic flow known as the KS model of turbulence, we investigate the dependence of Lyapunov exponents on various characteristics of the flow. We show that the KS model yields a power law relation between the Reynolds…
We introduce a family of hyperbolic flows on non-compact phase spaces that includes the geodesic flow on the modular surface. For these systems we prove exponential decay of correlations for sufficiently regular observables with respect to…
This paper is concerned with system of magnetic effected piezoelectric beams with interior time-varying delay and time-dependent weights, in which the beam is clamped at the two side points subject to a single distributed state feedback…
Bochi-Katok-Rodriguez Hertz proposed in [BKH21] a program on the flexibility of Lyapunov exponents for conservative Anosov diffeomorphisms, and obtained partial results in this direction. For conservative Anosov diffeomorphisms with strong…
We consider a nonlocal nonlinear model with fractional diffusion motivated by studies of electroconvection phenomena in incompressible viscous fluids. We address the global well-posedness, global regularity and long time dynamics of the…
In this article we investigate the existence, uniqueness and exponential decay of asymptotically almost periodic solutions of the parabolic-elliptic Keller-Segel system on a real hyperbolic manifold. We prove the existence and uniqueness of…
Long-lasting quantum exponential spreading was recently found in a simple but very rich dynamical model, namely, an on-resonance double-kicked rotor model [J. Wang, I. Guarneri, G. Casati, and J. B. Gong, Phys. Rev. Lett. 107, 234104…
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…
We prove that for any partially hyperbolic diffeomorphism with one dimensional neutral center on a 3-manifold, the center stable and center unstable foliations are complete; moreover, each leaf of center stable and center unstable…
We show that quasi-isometries of (well-behaved) hierarchically hyperbolic groups descend to quasi-isometries of their maximal hyperbolic space. This has two applications, one relating to quasi-isometry invariance of acylindrical…
We study the continuum percolation model, which is defined on $\mathbb{Z}^d\times \mathbb{R}$ so that the connections in the continuous directions are not oriented in time, with quasiperiodically disordered fields. The oriented version of…
In the framework of the rigged Hilbert space, unstable quantum systems associated with first order poles of the analytically continued S-matrix can be described by Gamow vectors which are generalized vectors with exponential decay and a…
Let $K$ be a complete discretely valued field. An extension $L/K$ is "weakly totally ramified" if the residue extension is purely inseparable. We sharpen a result of Ax by showing that any Galois-invariant disk in the algebraic closure of…
We state necessary and sufficient conditions for the existence of $T$-discrete exponential attractors for semigroups in complete metric spaces. These conditions are formulated in terms of a covering condition for iterates of the absorbing…
We consider the exactly soluble Edwards-Wilkinson Model in one dimension and demonstrate explicitly, that it is possible to construct a field, that does not depend explicitly on time, such that the corresponding time dependent correlation…
In this paper, we generalize the existence result in [14] and prove convergence theorems of the iterative scheme in [12, 16] for monotone generalized alpa-nonexpansive mappings in uniformly convex partially ordered hyperbolic metric spaces.…