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We characterize the representations of the fundamental group of a closed surface to $\mathrm{PSL}_2(\mathbb C)$ that arise as the holonomy of a branched complex projective structure with fixed branch divisor. In particular, we compute the…

We give a review of results on superpolynomial decay of correlations, and polynomial decay of correlations for nonuniformly expanding semiflows and nonuniformly hyperbolic flows. A self-contained proof is given for semiflows. Results for…

For Cartan geometries admitting automorphisms with isotropies satisfying a particular, loosely dynamical property on their model geometries, we demonstrate the existence of an open subset of the geometry with trivial holonomy. This…

An asymptotic expansion is established for time averages of translation flows on flat surfaces. This result, which extends earlier work of A.Zorich and G.Forni, yields limit theorems for translation flows. The argument, close in spirit to…

We prove a differential Harnack inequality for noncompact convex hypersurfaces flowing with normal speed equal to a symmetric function of their principal curvatures. This extends a result of Andrews for compact hypersurfaces. We assume that…

Exceptional points in non-Hermitian systems have recently been shown to possess nontrivial topological properties, and to give rise to many exotic physical phenomena. However, most studies thus far have focused on isolated exceptional…

We prove that the geodesic flow on closed surfaces displays a hyperbolic set if the shadowing property holds C2-robustly on the metric. Similar results are obtained when considering even feeble properties like the weak shadowing and the…

The questions of global topological, smooth and holomorphic classifications of the differential systems, defined by covering foliations, are considered. The received results are applied to nonautonomous linear differential systems and…

Hypersurfaces of manifolds of constant nonzero sectional curvature are classificated according their restricted homogeneous holonomy groups.

Bing and Moise proved, independently, that any Peano continuum admits a length metric d. We treat non-degenerate Peano continua with a length metric as evolution systems instead of stationary objects. For any compact length space (X, d) we…

We derive general depth-integrated model equations for overland flows featuring the evolution of suspended sediment that may be eroded from or deposited onto the underlying topography ('morphodynamics'). The resulting equations include…

On the space of positive 3-forms on a seven-manifold, we study a natural functional whose critical points induce metrics with holonomy contained in $G_2$. We prove short-time existence and uniqueness for its negative gradient flow.…

We classify hyperbolic polynomials in two real variables that admit a transitive action on some component of their hyperbolic level sets. Such surfaces are called special homogeneous surfaces, and they are equipped with a natural Riemannian…

We present a framework for modeling complex, high-dimensional distributions on convex polytopes by leveraging recent advances in discrete and continuous normalizing flows on Riemannian manifolds. We show that any full-dimensional polytope…

Piecewise Euclidean structures (identified solid Euclidean polyhedra) on topological 3-dimensional manifolds and pseudo-manifolds are constructed so that they admit pseudo-foliations, a generalized type of foliation. The construction of…

We present some constructions that are merely the fruit of combining recent results from two areas of smooth dynamics: nonuniformly hyperbolic systems and elliptic constructions.

We study fully nonlinear geometric flows that deform strictly $k$-convex hypersurfaces in Euclidean space with pointwise normal speed given by a concave function of the principal curvatures. Specifically, the speeds we consider are obtained…

The paper deals with singularities of nonconfluent hypergeometric functions in several variables. Typically such a function is a multi-valued analytic function with singularities along an algebraic hypersurface. We describe such…

The aim of this paper is to establish exponential mixing of frame flows for convex cocompact hyperbolic manifolds of arbitrary dimension with respect to the Bowen-Margulis-Sullivan measure. Some immediate applications include an asymptotic…

We study the length-preserving elastic flow of curves in arbitrary codimension with free boundary on hypersurfaces. This constrained gradient flow is given by a nonlocal evolution equation with nonlinear higher-order boundary conditions. We…