Related papers: Topological stability for conservative systems
This paper is concerned with the mathematical derivation of the inhomoge-neous incompressible Navier-Stokes equations (INS) from the compressible Navier-Stokes equations (CNS) in the large volume viscosity limit. We first prove a result of…
Our context is Filippov systems defined on two-dimensional manifolds having a finite number of tangency points. We prove that topological transitivity is a necessary and sufficient condition for the occurrence of non-deterministic chaos…
In this paper, it is shown that the set consisting of stable convex integrands $S^n\to \mathbb{R}_+$ is open and dense in the set consisting of $C^\infty$ convex integrands with respect to Whitney $C^\infty$ topology. Moreover, an…
In this paper, we study the linear stability of Couette flow for 2D compressible Navier-Stokes-Poisson system at high Reynolds number in the domain $\mathbb{T}\times\mathbb{R}$ with initial perturbation in Sobolev spaces. We establish the…
A set of necessary conditions for $C^1$ stability of noninvertible maps is presented. It is proved that the conditions are sufficient for $C^1$ stability in compact oriented manifolds of dimension two. An example given by F.Przytycki in…
We prove that non-trivial homoclinic classes of $C^r$-generic flows are topologically mixing. This implies that given $\Lambda$ a non-trivial $C^1$-robustly transitive set of a vector field $X$, there is a $C^1$-perturbation $Y$ of $X$ such…
Two flows are topologically almost commensurable if, up to removing finitely many periodic orbits and taking finite coverings, they are topologically equivalent. We prove that all suspensions of automorphisms of the 2-dimensional torus and…
We show that any $(\C ^*)^n$-invariant stably complex structure on a topological toric manifold of dimension $2n$ is integrable. We also show that such a manifold is weakly $(\C ^*)^n$-equivariantly isomorphic to a toric manifold.
We establish a rigidity result for the unstable foliations of transitive Anosov flows on 3-manifolds: if the unstable foliations of two such flows are equivalent (that is, if there exists a homeomorphism mapping one foliation to the other),…
We prove three formulas for computing topological pressure of $C^1$-generic conservative diffeomorphism and show the continuity of topological pressure with respect to these diffeomorphisms. We prove for these generic diffeomorphisms that…
Let S be an ergodic measure-preserving automorphism on a non-atomic probability space, and let T be the time-one map of a topologically weak mixing suspension flow over an irreducible subshift of finite type under a Holder ceiling function.…
We give the complete classification of regular projectively Anosov flows on closed three-dimensional manifolds. More precisely, we show that such a flow must be either an Anosov flow or decomposed into a finite union of $T^2 \times…
We give complete classification of C^2-regular and non-degenerate projectively Anosov flows on three dimensional manifolds. More precisely, we prove that such a flow on a connected manifold must be either an Anosov flow or represented as a…
Let $f$ be a non-invertible irreducible Anosov map on $d$-torus. We show that if the stable bundle of $f$ is one-dimensional, then $f$ has the integrable unstable bundle, if and only if, every periodic point of $f$ admits the same Lyapunov…
In this paper we prove the asymptotic stability of the Kolmogorov flow on a non-square torus for perturbations $\omega_0$ satisfying $\|\omega_0\|_{H^3}\ll\nu^{1/3}$, where $0<\nu\ll1$ is the viscosity. Kolmogorov flows are important…
We are concerned with the linear stability of the Couette flow for the non-isentropic compressible Navier-Stokes equations with vanished shear viscosity in a domain $\mathbb{T}\times \mathbb{R}$. For a general initial data settled in…
We show that small perturbations of the spatially homogeneous equilibrium of a thermally driven compressible viscous fluid are globally stable. Specifically, any weak solution of the evolutionary Navier--Stokes--Fourier system driven by…
A {\em sectional-Anosov flow} is a vector field on a compact manifold inwardly transverse to the boundary such that the maximal invariant set is sectional-hyperbolic (in the sense of \cite{mm}). We prove that any $C^2$ transitive…
We introduce four, a priori different, notions of topological pressure for possibly discontinuous semiflows acting on compact metric spaces and observe that they all agree with the classical one when restricted to the continuous setting.…
The basic model for incompressible two-phase flows with phase transitions is derived from basic principles and shown to be thermodynamically consistent in the sense that the total energy is conserved and the total entropy is nondecreasing.…