Related papers: Proof of Wojtkowski's Falling Particle Conjecture
We use entropy theory as a new tool to study sectional hyperbolic flows in any dimension. We show that for $C^1$ flows, every sectional hyperbolic set $\Lambda$ is entropy expansive, and the topological entropy varies continuously with the…
Building upon previous works by Young, Chernov-Zhang and Bruin-Melbourne-Terhesiu, we present a general scheme to improve bounds on the statistical properties (in particular, decay of correlations, and rates in the almost sure invariant…
We study weakly hyperbolic iterated function systems on compact spaces, as defined by Edalat, but in the more general setting of a compact parameter space. We prove the existence of attractors, both in the topological and measure…
We prove that a weakly ergodic, eventually strong Feller semigroup on the space of measures on a Polish space converges strongly to a projection onto its fixed space.
In this paper, we study Wicksell's corpuscle problem in spaces of constant curvature, thus extending the classical Euclidean framework. We consider a particle process of balls with random radii in such a space, assumed to be invariant under…
A recent result of Downarowicz and Serafin (DS) shows that there exist positive entropy subshifts satisfying the assertion of Sarnak's conjecture. More precisely, it is proved that if $y=(y_n)_{n\ge 1}$ is a bounded sequence with zero…
Motivated by studying stochastic systems with non-Gaussian L\'evy noise, spectral properties for a type of linear cocycles are considered. These linear cocycles have countable jump discontinuities in time. A multiplicative ergodic theorem…
In this paper we derive a new first-order theory of relativistic dissipative fluids by adopting the trace-fixed particle frame. Whereas in a companion letter we show that this theory is hyperbolic, causal and stable at global equilibrium…
The rate of quantum ergodicity is studied for three strongly chaotic (Anosov) systems. The quantal eigenfunctions on a compact Riemannian surface of genus g=2 and of two triangular billiards on a surface of constant negative curvature are…
We demonstrate that Pleba\'nski's first heavenly equation decouples in infinitely many ways into a triple of commuting (1+1)-dimensional systems of hydrodynamic type which satisfy the Egorov property. Solving these systems by the…
We show that the system of equations describing a magnetoviscoelastic fluid in three dimensions can be cast as a quasilinear parabolic system. Using the theory of maximal $L_p$-regularity, we establish existence and uniqueness of local…
Modern advances in transformation optics and electromagnetic metamaterials made possible experimental demonstrations of highly unusual curvilinear optical spaces, such as various geometries necessary for electromagnetic cloaking. Recently…
We present a new route to ergodicity breaking via Hilbert space fragmentation that displays an unprecedented level of robustness. Our construction relies on a single emergent (prethermal) conservation law. In the limit when the conservation…
We obtain a dichotomy for $C^1$-generic symplectomorphisms: either all the Lyapunov exponents of almost every point vanish, or the map is partially hyperbolic and ergodic with respect to volume. This completes a program first put forth by…
In this paper, we give a precise meaning to the following fact, and we prove it: $C^1$-open and densely, all the non-hyperbolic ergodic measures generated by a robust cycle are approximated by periodic measures. We apply our technique to…
Electrodynamic phenomena related to vortices in superconductors have been studied since their prediction by Abrikosov, and seem to hold no fundamental mysteries. However, most of the effects are treated separately, with no guiding…
We find a normal form which describes the high energy dynamics of a class of piecewise smooth Fermi-Ulam ping pong models; depending on the value of a single real parameter, the dynamics can be either hyperbolic or elliptic. In the first…
We prove a ratio ergodic theorem for non-singular free $Z^d$ and $R^d$ actions, along balls in an arbitrary norm. Using a Chacon-Ornstein type lemma the proof is reduced to a statement about the amount of mass of a probability measure that…
In this paper we prove that the motion of a solid body in a two dimensional incompressible perfect fluid converges, when the body shrinks to a point with fixed mass and circulation, to a variant of the vortex-wave system where the vortex,…
This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology,…