相关论文: Lyapunov exponents and Hodge theory

Hodge correlators are complex numbers given by certain integrals assigned to a smooth complex curve. We show that they are correlators of a Feynman integral, and describe the real mixed Hodge structure on the pronilpotent completion of the…

We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case.…

This paper is concerned with the Lyapunov spectrum for measurable cocycles over an ergodic pmp system taking values in semi-simple real Lie groups. We prove simplicity of the Lyapunov spectrum and its continuity under certain perturbations…

Explicit symplectic integrators have been important tools for accurate and efficient approximations of mechanical systems with separable Hamiltonians. For the first time, the article proposes for arbitrary Hamiltonians similar integrators,…

We show that there is a residual subset $\mathcal{R}$ of $Diff^1(M)$ such that for any $f\in\mathcal{R}$ and any partially hyperbolic homoclinic class $H(p,f)$ with one dimensional center direction, the set of central Lyapunov exponents…

Lyapunov exponents describe the asymptotic behavior of the singular values of large products of random matrices. A direct computation of these exponents is however often infeasible. By establishing a link between Lyapunov exponents and an…

We study nonhyperbolic and transitive partially hyperbolic diffeomorphisms having a one-dimensional center. We prove joint flexibility with respect to entropy and center Lyapunov exponent for a broad class of these systems. Flexibility…

We review some of the properties of higher-dimensional superstatistical stochastic models. As an example, we analyse the stochastic properties of a superstatistical model of 3-dimensional Lagrangian turbulence, and compare with experimental…

We prove that for semi-invertible and H\"older continuous linear cocycles $A$ acting on an arbitrary Banach space and defined over a base space that satisfies the Anosov Closing Property, all exceptional Lyapunov exponents of $A$ with…

The phase space trajectories of many body systems charateristic of simple fluids are highly unstable. We quantify this instability by a set of Lyapunov exponents, which are the rates of exponential divergence, or convergence, of initial…

We study the ergodic properties of compositions of interval exchange transformations and rotations. We show that for any interval exchange transformation T, there is a full measure set of \alpha in [0, 1) so that T composed with R_{\alpha}…

This expository paper, based on a Current Events Bulletin talk at the January, 2016 Joint Meetings, introduces the concept of Lyapunov exponents and discusses the role they play in three areas: smooth ergodic theory, Teichm\"uller theory,…

We conjecture that there exists a relationship between Lyapunov exponents and black hole phase transitions. To support our conjecture, Lyapunov exponents of the motion of particles and ring strings are calculated for…

We show how the Lyapunov exponents of a dynamic system can in general be expressed in terms of the free energy of a (non-Hermitian) quantum many-body problem. This puts their study as a problem of statistical mechanics, whose intuitive…

A general method to determine covariant Lyapunov vectors in both discrete- and continuous-time dynamical systems is introduced. This allows to address fundamental questions such as the degree of hyperbolicity, which can be quantified in…

We investigate the predictability problem in dynamical systems with many degrees of freedom and a wide spectrum of temporal scales. In particular, we study the case of $3D$ turbulence at high Reynolds numbers by introducing a finite-size…

A class of elliptic-hyperbolic equations is placed in the context of a geometric variational theory, in which the change of type is viewed as a change in the character of an underlying metric. A fundamental example of a metric which changes…

We study the connection between the exponent of the order parameter of the Mott insulator-to-superfluid transition occurring in the two-dimensional Bose-Hubbard model, and the divergence exponents of its one- and two-particle correlation…

A geometric interpretation is given for certain elliptic-hyperbolic systems in the plane. Among several examples, one which reduces in the elliptic region to the equations for harmonic 1-forms on the projective disc is studied in detail. A…

In the framework of statistical mechanics the properties of macroscopic systems are deduced starting from the laws of their microscopic dynamics. One of the key assumptions in this procedure is the ergodic property, namely the equivalence…