相关论文: Polynomial entropy for the circle homeomorphisms a…
We show that the polynomial entropy of homeomorphisms on regular curves is bounded above by one. Moreover, the polynomial entropy equals one under the fairly mild condition that the homeomorphism possesses a wandering point. We obtain a…
We compute the polynomial entropy of $C(f)$ where $f$ is any circle homeomorphism.
In this paper we study the polynomial entropy of homeomorphism on compact metric space. We construct a homeomorphism on a compact metric space with vanishing polynomial entropy that it is not equicontinuous. Also we give examples with…
We study the polynomial entropy of the wandering part of any invertible dynamical system on a compact metric space. As an application we compute the polynomial entropy of Brouwer homeomorphisms (fixed point free orientation preserving…
We compute the polynomial entropy of the induced maps on hyperspace for a homeomorphism $f$ of an interval or a circle with finitely many non-wandering points.
Two flows defined on a smooth manifold are equivalent if there exists a homeomorphism of the manifold that sends each orbit of one flow onto an orbit of the other flow while preserving the time orientation. The topological entropy of a flow…
We prove the following dichotomy for vector fields in a C1-residual subset of volume-preserving flows: for Lebesgue almost every point all Lyapunov exponents equal to zero or its orbit has a dominated splitting. As a consequence if we have…
In this paper, we study the entropy of a Hamiltonian flow in restriction to an enregy level where it admits a first integral which is nondegenerate in the Bott sense. It is easy to see that for such a flow, the topological entropy vanishes.…
We prove that every $C^1$ three-dimensional flow with positive topological entropy can be $C^1$ approximated by flows with homoclinic orbits. This extends a previous result for $C^1$ surface diffeomorphisms \cite{g}.
Given any $K>0$, we construct two equivalent $C^2$ flows, one of which has positive topological entropy larger than $K$ and admits zero as the exponential growth of periodic orbits, in contrast, the other has zero topological entropy and…
We give a simple proof of a classical theorem by A.M\'at\'e, P.Nevai, and V.Totik on asymptotic behavior of orthogonal polynomials on the unit circle. It is based on a new real-variable approach involving an entropy estimate for the…
We show that if $f$ is an annular homeomorphism admitting an attractor which is an irreducible annular continua with two different rotation numbers, then the entropy of $f$ is positive. Further, the entropy is shown to be associated to a…
We introduce the notion of a one-way horseshoe and show that the polynomial entropy of an interval map is given by one-way horseshoes of iterates of the map, obtaining in such a way an analogue of Misiurewicz's theorem on topological…
Consider the set $\chi^0_{\mathrm{nw}}$ of non-wandering continuous flows on a closed surface. Then such a flow can be approximated by regular non-wandering flows without heteroclinic connections nor locally dense orbits in…
We study the topological entropy of the magnetic flow on a closed riemannian surface. We prove that if the magnetic flow has a non-hyperbolic closed orbit in some energy set T^cM= E^{-1}(c), then there exists an exact $…
We prove that the polynomial entropy of the induced map $F_n(f)$ on the $n$-fold symmetric product of a compact space $X$ and its suspension are both equal to $nh_{pol}(f)$, when $f:X\to X$ is a homeomorphism with a finite chain recurrent…
We define a notion of entropy for an infinite family $\mathcal{C}$ of measurable sets in a probability space. We show that the mean ergodic theorem holds uniformly for $\mathcal{C}$ under every ergodic transformation if and only if…
It is proved that whenever two aperiodic repetitive tilings with finite local complexity have homeomorphic tiling spaces, their associated complexity functions are asymptotically equivalent in a certain sense (which implies, if the…
A classical construction due to Newhouse creates horseshoes from hyperbolic periodic orbits with large period and weak domination through local $C^1$-perturbations. Our main theorem shows that, when one works in the $C^1$ topology, the…
We study the unstable entropy of $C^1$ diffeomorphisms with dominated splittings. Our main result shows that when the zero Lyapunov exponent has multiplicity one, the center direction contributes no entropy, and the unstable entropy…