相关论文: Dynamical classification of analytic one-frequency…

In this paper we study perturbations of constant cocycles for actions of higher rank semi-simple algebraic groups and their lattices. Roughly speaking, for ergodic actions, Zimmer's cocycle superrigidity theorems implies that the perturbed…

The analysis of a timeseries can provide many new perspectives if it is accompanied by the assumption that the timeseries is generated from an underlying dynamical system. For example, statistical properties of the data can be related to…

We define a variant of the Young integration on some kinds of self-similar sets which are called cellular self-similar sets. This variant is an analogue of the Young integration defined on the unit interval. We give the criteria of the…

We study the dynamics of the three-dimensional polaron - a quantum particle coupled to bosonic fields - in the quasi-classical regime. In this case the fields are very intense and the corresponding degrees of freedom can be treated…

In the framework of SOS models, the dynamics of isolated and pairs of surface steps of monoatomic height is studied, for step--edge diffusion and for evaporation kinetics, using Monte Carlo techniques. In particular, various interesting…

We consider compact connected six dimensional symplectic manifolds with Hamiltonian SU(2) or SO(3) actions with cyclic principal stabilizers. We classify such manifolds up to equivariant symplectomorphisms.

We study pseudo-simple heteroclinic cycles for a $\Gamma$-equivariant system in $R^4$ with finite $\Gamma\subset O(4)$, and their nearby dynamics. In particular, in a first step towards a full classification - analogous to that which exists…

Following an old suggestion of M. Kontsevich, and inspired by recent work of A. Beilinson and B. Bhatt, we introduce a new version of periodic cyclic homology for DG agebras and DG categories. We call it co-periodic cyclic homology. It is…

A host of dynamical measures of quantum correlations -- out-of-time ordered correlators (OTOC), Loschmidt echo, generalized entanglement and observational entropy -- are useful to infer the underlying classical chaotic dynamics in quantum…

We prove rotations-reducibility for close to constant quasi-periodic $SL(2,\mathbb{R})$ cocycles in one frequency in the finite regularity and smooth cases, and derive some applications to quasi-periodic Schr\"odinger operators.

The Conley theory has a tool to guarantee the existence of periodic trajectories in isolating neighborhoods of semi-dynamical systems. We prove that the positive trajectories generated by a piecewise-smooth vector field $Z=(X, Y)$ defined…

The coupled Stuart-Landau equation serves as a fundamental model for exploring synchronization and emergent behavior in complex dynamical systems. However, understanding its dynamics from a comprehensive nonlinear perspective remains…

We consider an open and dense subset of the set of all connections (heteroclinic orbits) between two saddles of a vector field in dimension three. We give a complete classification up to topological equivalence of the dynamics in a…

We study localisation transition in a class of quasi-periodic systems that has two competing periodic scales. We show that such class of systems show a re-entrant localisation transition where the energy scale of transition is set by the…

We develop a theory of differential equations associated to families of algebraic cycles in higher Chow groups (i.e., motivic cohomology groups). This formalism is related to inhomogeneous Picard--Fuchs type differential equations. For…

We define families of invariants for elements of the mapping class group of S, a compact orientable surface. Fix any characteristic subgroup H of pi_1(S) and restrict to J(H), any subgroup of mapping classes that induce the identity modulo…

We consider a one-dimensional gas of hard rods, one of the simplest examples of an interacting integrable model. It is well known that the hydrodynamics of such integrable models can be understood by viewing the system as a gas of…

The level statistics of pseudointegrable fractal drums is studied numerically using periodic orbit theory. We find that the spectral rigidity $\Delta_3(L)$, which is a measure for the correlations between the eigenvalues, decreases to quite…

We construct a nontrivial cyclic cocycle on the Weyl algebra of a symplectic vector space. Using this cyclic cocycle we construct an explicit, local, quasi-isomorphism from the complex of differential forms on a symplectic manifold to the…

LSST is expected to yield ~10^7 light curves over the course of its mission, which will require a concerted effort in automated classification. Stochastic processes provide one means of quantitatively describing variability with the…