Related papers: $C^1$ Robust Rigidity for Bi-critical Circle Maps

We present sufficient conditions so that a conformal map between planar domains whose boundary components are Jordan curves or points has a continuous or homeomorphic extension to the closures of the domains. Our conditions involve the…

The conjugacy problem is one of the central questions in iteration theory. As far as we, for discontinuous strictly monotone maps there is no complete result. In this paper, we investigate the conjugacy problem of strictly monotone maps…

A gap mapping is a discontinuous interval mapping with two strictly increasing branches that have a gap between their ranges. They are one-dimensional dynamical systems, which arise in the study of certain higher dimensional flows, for…

We exhibit a new large class of $C^1$ open examples of robustly transitive maps displaying persistent critical points in the homotopy class of expanding endomorphisms acting on the two dimensional Torus and the Klein bottle.

We describe a new and robust method to prove rigidity results in complex dynamics. The new ingredient is the geometry of the critical puzzle pieces: under control of geometry and ``complex bounds'', two generalized polynomial-like maps…

We prove that curve complexes of surfaces are finitely rigid: for every orientable surface S of finite topological type, we identify a finite subcomplex X of the curve complex C(S) such that every locally injective simplicial map from X…

The goal of this article is to show a rigidity property of conjugacies of generalized interval exchange transformations (GIETs). More precisely, we show that if two piecewise $C^3$ GIETs $f$ and $g$ of generic rotation number with…

This paper deals with the renormalization of symmetric bimodal maps with low smoothness. We prove the existence of the renormalization fixed point in the space $C^{1+Lip}$ symmetric bimodal maps. Moreover, we show that the topological…

Topological conjugateness of one dimensional unimodal dynamical systems, which are generated by interval [0, 1] into itself maps are studied. We study the smoothness and differentiability of the conjugacy of symmetrical and non-symmetrical…

We study the notions of continuous orbit equivalence and eventual one-sided conjugacy of finitely-aligned higher-rank graphs and two-sided conjugacy of row-finite higher-rank graphs with finitely many vertices and no sinks or sources. We…

The CR analogue of B.-Y. Chen's conjecture on pseudo biharmonic maps will be shown. Pseudo biharmonic, but not pseudo harmonic, isometric immersions with parallel pseudo mean curvature vector fields, will be characterized. Several examples…

It is shown that some topological equivalency classes of S-unimodal maps are equal to quasisymmetric conjugacy classes. This includes some infinitely renormalizable polynomials of unbounded type.

In this paper we prove C^k structure stability conjecture for unimodal maps. In other words, we shall prove that Action A maps are dense in the space of C^k unimodal maps in the C^k topology. Here k can be 1,2,...,\infty,\omega.

We introduce a class of infinitely renormalizable, unicritical diffeomorphisms of the disk (with a non-degenerate "critical point"). In this class of dynamical systems, we show that under renormalization, maps eventually become…

We prove that, on connected compact manifolds, both C1-generic conservative diffeomorphisms and C1-generic transitive diffeomorphisms are topologically mixing. This is obtained through a description of the periods of a homoclinic class and…

In this paper, we give a complete topological and smooth classification of non-invertible Anosov maps on torus. We show that two non-invertible Anosov maps on torus are topologically conjugate if and only if their corresponding periodic…

Biharmonic maps between surfaces are studied in this paper. We compute the bitension field of a map between surfaces with conformal metrics in complex coordinates. As applications, we show that a linear map from Euclidean plane into…

We prove that a topological homeomorphism conjugating two generic 1-parameter unfoldings of 1-variable complex analytic resonant diffeomorphisms is holomorphic or anti-holomorphic by restriction to the unperturbed parameter. We provide…

For each piecewise linear Lorenz map that expand on average, we show that it admits a dichotomy: it is either periodic renormalizable or prime. As a result, such a map is conjugate to a $\beta$-transformation.

We show that the topological classification and the smooth classification are generically the same for certain families of plane curves in a semi-local case(the double local case). Especially we give the normal form of transversely jointed…