相关论文: An Analytical Construction of the SRB Measures for…

We consider a stochastic conservation law on the line with solution-dependent diffusivity, a super-linear, sub-quadratic Hamiltonian, and smooth, spatially-homogeneous kick-type random forcing. We show that this Markov process admits a…

In the study of non-equilibrium statistical mechanics, Ruelle derived explicit formulae for entropy production of smooth dynamical systems. The vanishing or strict positivity of entropy production is determined by the {\it entropy formula…

In this paper, we consider the dynamics of a skew-product map defined on the Cartesian product of the symbolic one-sided shift space on $N$ symbols and the complex sphere where we allow $N$ rational maps, $R_{1}, R_{2}, \cdots, R_{N}$, each…

The method of regularized Stokeslets (MRS) is a numerical approach using regularized fundamental solutions to compute the flow due to an object in a viscous fluid where inertial effects can be neglected. The elastic object is represented as…

The scaled Brownian motion (SBM) is regarded as one of the paradigmatic random processes, featuring the anomalous diffusion property characterized by the diffusion exponent. It is a Gaussian, self-similar process with independent…

We consider a two-parameter family of maps $T_{\alpha, \beta}: [0,1] \to [0,1]$ with a neutral fixed point and a non-flat critical point. Building on a cone technique due to Baladi and Todd, we show that for a class of $L^q$ observables…

We prove the abundance of Sinai-Ruelle-Bowen measures for diffeomorphisms away from ones with a homoclinic tangency. This is motivated by conjectures of Palis on the existence of physical (Sinai-Ruelle-Bowen) measures for global dynamics.…

Limit theorems for the time average of some observation functions in an infinite measure dynamical system are studied. It is known that intermittent phenomena, such as the Rayleigh-Benard convection and Belousov-Zhabotinsky reaction, are…

We study hyperbolic skew products and the disintegration of the SRB measure into measures supported on local stable manifolds. Such a disintegration gives a method for passing from an observable $v$ on the skew product to an observable…

Constructing flexible probability models that respect constraints on key functionals -- such as the mean -- is a fundamental problem in nonparametric statistics. Existing approaches lack systematic tools for enforcing such constraints while…

We consider the family of Henon maps in the plane and show that the SRB measures vary continuously in the weak* topology within the set of Benedicks-Carleson parameters.

We prove that, under some natural conditions, Hamiltonian systems on a contact manifold $C$ can be split into a Reeb dynamics on an open subset of $C$ and a Liouville dynamics on a submanifold of $C$ of codimension 1. For the Reeb dynamics…

We consider the dynamics of skew product maps associated with finitely generated semigroups of rational maps on the Riemann sphere. We show that under some conditions on the dynamics and the potential function \psi, there exists a unique…

In this paper, we construct a digraph structure on $p$-adic dynamical systems defined by rational functions. We study the conditions under which the functions are measure-preserving, invertible and isometric, ergodic, and minimal on…

We introduce the Markov extension, represented schematically as a tower, to the study of dynamical systems with holes. For tower maps with small holes, we prove the existence of conditionally invariant probability measures which are…

This paper investigates asymptotic behavior of a stochastic SIR epidemic model, which is a system with degenerate diffusion. It gives sufficient conditions that are very close to the necessary conditions for the permanence. In addition,…

Let $ R $ be a rational map. We are interesting in the dynamic of the Ruelle operator on suitable spaces of differentials. In particular the necessary and sufficient conditions (in terms of convergence of sequences of measures) of existence…

We develop a quenched thermodynamic formalism for a wide class of random maps with non-uniform expansion, where no Markov structure, no uniformly bounded degree or the existence of some expanding dynamics is required. We prove that every…

Reversible cellular automata are seen as microscopic physical models, and their states of macroscopic equilibrium are described using invariant probability measures. We establish a connection between the invariance of Gibbs measures and the…

The paper introduces a general method to construct conformal measures for a local homeomorphism on a locally compact non-compact Hausdorff space, subject to mild irreducibility-like conditions. Among others the method is used to give…