Related papers: Differentiation of SRB states for hyperbolic flows
We study the Ricci flow of initial metrics which are C^0-perturbations of the hyperbolic metric on H^n. If the perturbation is bounded in the L^2-sense, and small enough in the C^0-sense, then we show the following: In dimensions four and…
The paper addresses the numerical approximation of two variants of hyperbolic mean curvature flow of surfaces in $\mathbb R^3$. For each evolution law we propose both a finite element method, as well as a finite difference scheme in the…
We investigate a new type of approximation to quantum determinants, the ``\qFd", and test numerically the conjecture that for Axiom A hyperbolic flows such determinants have a larger domain of analyticity and better convergence than the \qS…
A simple and transparent example of a non-autonomous flow system, with hyperbolic strange attractor is suggested. The system is constructed on a basis of two coupled van der Pol oscillators, the characteristic frequencies differ twice, and…
We numerically demonstrate the feasibility of kinematic fast dynamos for a class of time-periodic axisymmetric flows of conducting fluid confined inside a sphere. The novelty of our work is in considering the realistic flows, which are…
Solute dispersion due to an instantaneously released source in steady, laminar, axisymmetric flows with an axial inflow and radial outflow is investigated analytically. Attention is given to large-time characteristics of dispersion, where…
We show that for every non-elementary hyperbolic group the Bowen-Margulis current associated with a strongly hyperbolic metric forms a unique group-invariant Radon measure class of maximal Hausdorff dimension on the boundary square.…
Stars and planets move supersonically in a gaseous medium during planetary engulfment, stellar interactions and within protoplanetary disks. For a nearly uniform medium, the relevant parameters are the Mach number and the size of the body,…
Singular and sectional hyperbolic sets are the objects of the extension of the classical Smale Hyperbolic Theory to flows having invariant sets with singularities accumulated by regular orbits within the set. It is by now well-known that…
We obtain a exponential large deviation upper bound for continuous observables on suspension semiflows over a non-uniformly expanding base transformation with non-flat singularities and/or discontinuities, where the roof function defining…
In this paper we study the following stochastic Hamiltonian system in ${\mathbb R}^{2d}$ (a second order stochastic differential equation), $$ d \dot X_t=b(X_t,\dot X_t)d t+\sigma(X_t,\dot X_t)d W_t,\ \ (X_0,\dot X_0)=(x,v)\in{\mathbb…
We consider partially hyperbolic attractors for non-singular endomorphisms admitting an invariant stable bundle and a positively invariant cone field with non-uniform cone expansion at a positive Lebesgue measure set of points. We prove…
Under mild assumptions, the SRB measure $\mu$ associated to an Axiom A attractor $A$ has the following properties: (i) the empirical measure starting at a typical point near $A$ converges weakly to $\mu$; (ii) the pushforward of any…
In this paper, we study the existence of SRB measures for infinite dimensional dynamical systems in a Banach space. We show that if the system has a partially hyperbolic attractor with nontrivial finite dimensional unstable directions, then…
There exists a $C^2$-open and $C^1$-dense subset of vector fields exhibiting singular-hyperbolic attracting sets (with codimension-two stable bundle), in any $d$-dimensional compact manifold ($d\ge3$), which mix exponentiallu with respect…
We define a quantitative notion of shear for limit cycles of flows. We prove that strange attractors and SRB measures emerge when systems exhibiting limit cycles with sufficient shear are subjected to periodic pulsatile drives. The strange…
We introduce the functor * which assigns to every metric space X its symmetric join *X. As a set, *X is a union of intervals connecting ordered pairs of points in X. Topologically, *X is a natural quotient of the usual join of X with…
We derive a criterion for the breakdown of solutions to the Oldroyd-B model in $\R^3$ in the limit of zero Reynolds number (creeping flow). If the initial stress field is in the Sobolev space $H^m$, $m> 5/2$, then either a unique solution…
We give a definition of the spectral flow for continuous paths in the space of bounded and essentially hyperbolic operators. We provide a homotopical characterization of the spectral flow in terms of a group homomorphism of the fundamental…
For sufficiently slow rates of strain, flowing foam can exhibit inhomogeneous flows. The nature of these flows is an area of active study in both two-dimensional model foams and three dimensional foam. Recent work in three-dimensional foam…