Related papers: Polynomial entropy for the circle homeomorphisms a…
We obtain a $C^1$-generic subset of the incompressible flows in a closed three-dimensional manifold where Pesin's entropy formula holds thus establishing the continuous-time version of \cite{T}. Moreover, in any compact manifold of…
The geodesic flow of the flat metric on a torus is minimizing the polynomial entropy among all geodesic flows on this torus. We prove here that this properties characterises the flat metric on the two torus.
We study nontrivial entropy invariants in the class of parabolic flows on homogeneous spaces, quasi-unipotent flows. We show that topological complexity (ie, slow entropy) can be computed directly from the Jordan block structure of the…
The aim of this paper is to state and prove polynomial analogues of the classical Manning inequality relating the topological entropy of a geodesic flow with the growth rate of the volume of balls in the universal covering. To this aim we…
If a real-analytic flow on the multidimensional torus close enough to linear has a unique rotation vector which satisfies an arithmetical condition Y, then it is analytically conjugate to linear. We show this by proving that the orbit under…
We study basic properties of flow equivalence on one-dimensional compact metric spaces with a particular emphasis on isotopy in the group of (self-) flow equivalences on such a space. In particular, we show that an orbit-preserving such map…
Let f be a homeomorphism of the torus isotopic to the identity and suppose that there exists a periodic orbit with a non-zero rotation vector (p/q,r/q), then f has a topologically monotone periodic orbit with the same rotation vector.
In this work we develop a new criterion for the existence of topological horseshoes for surface homeomorphisms in the isotopy class of the identity. Based on our previous work on forcing theory, this new criterion is purely topological and…
The periodic orbit conjecture states that, on closed manifolds, the set of lengths of the orbits of a non-vanishing vector field all whose orbits are closed admits an upper bound. This conjecture is known to be false in general due to a…
As defined by W. Thurston, the core entropy of a polynomial is the entropy of the restriction to its Hubbard tree. For each d >= 2, we study the core entropy as a function on the parameter space of polynomials of degree d, and prove it…
Steady fluid flows have very special topology. In this paper we describe necessary and sufficient conditions on the vorticity function of a 2D ideal flow on a surface with or without boundary, for which there exists a steady flow among…
For any $C^\infty$, area-preserving Anosov diffeomorphism $f$ of a surface, we show that a suspension flow over $f$ is $C^\infty$-conjugate to a constant-time suspension flow of a hyperbolic automorphism of the two torus if and only if the…
The following numerical control over the topological equivalence is proved: two complex polynomials in $n\not= 3$ variables and with isolated singularities are topologically equivalent if one deforms into the other by a continuous family of…
For some full measure subset B of the set of iet's (i.e. interval exchange transformations) the following is satisfied: Let X be a $C^r$, $1\le r\le \infty$, vector field, with finitely many singularities, on a compact orientable surface M.…
We study the topological entropy of a two-parameter family of maps related to (a,b)-continued fraction algorithms and prove that it is constant on a square within the parameter space (two vertices of this square correspond to well-studied…
We use entropy theory as a new tool for studying Lorenz-like classes of flows in any dimension. More precisely, we show that every Lorenz-like class is entropy expansive, and has positive entropy which varies continuously with vector…
We prove that a vector field on an affine $C^\infty$-scheme Spec(A) has a flow if the $C^\infty$-ring A is finitely generated. If the vector field is complete then the flow is the target map of a groupoid internal to the category of…
In this article we study the regularity of the topological and metric entropy of partially hyperbolic flows with two-dimensional center direction. We show that the topological entropy is upper semicontinuous with respect to the flow, and we…
The relative entropy in two-dimensional field theory is studied on a cylinder geometry, interpreted as finite-temperature field theory. The width of the cylinder provides an infrared scale that allows us to define a dimensionless relative…
Given ergodic p-invariant measures {\mu_i} on the 1-torus T=R/Z, we give a sharp condition on their entropies, guaranteeing that the entropy of the convolution \muon converges to \log p. We also prove a variant of this result for joinings…