相关论文: One-dimensional maps and Poincar\'e metric

For two-parameter families of dissipative twist maps, we investigate the dynamics of invariant graphs as well as the thresholds for their existence and breakdown. Our main results are as follows: (1) For arbitrarily small $C^r$…

A method is proposed for the calculation of diffusion constants for one-dimensional maps exhibiting deterministic diffusion. The procedure is based on harmonic inversion and uses a known relation between the diffusion constant and the…

This paper will study topological, geometrical and measure-theoretical properties of the real Fibonacci map. Our goal was to figure out if this type of recurrence really gives any pathological examples and to compare it with the infinitely…

We introduce an infinite sequence of higher order Schwarzian derivatives closely related to the theory of monotone matrix functions. We generalize the classical Koebe lemma to maps with positive Schwarzian derivatives up to some order,…

In this paper, we consider mappings on uniform domains with exponentially integrable distortion whose Jacobian determinants are integrable. We show that such mappings can be extended to the boundary and moreover these extensions are…

We prove that if the Schwarzian norm of a given complex-valued locally univalent harmonic mapping $f$ in the unit disk is small enough, then $f$ is, indeed, globally univalent and can be extended to a quasiconformal mapping in the extended…

We prove strong statistical stability of a large class of one-dimensional maps which may have an arbitrary finite number of discontinuities and of non-degenerate critical points and/or singular points with infinite derivative, and satisfy…

We study diffeomorphisms that have one-parameter families of continuous symmetries. For general maps, in contrast to the symplectic case, existence of a symmetry no longer implies existence of an invariant. Conversely, a map with an…

For piecewise $C^1$ interval maps possibly containing critical points and discontinuities with negative Schwarzian derivative, under two summability conditions on the growth of the derivative and recurrence along critical orbits, we prove…

In this survey we present the history and recent progress on several fundamental (quasi)conformal uniformization problems in the complex plane. Uniformization refers to the process of mapping a space to a canonical model by means of a…

Perturbations due to round-off errors in computer modeling are discontinuous and therefore one cannot use results like KAM theory about smooth perturbations of twist maps. We elaborate a special approximation scheme to construct two smooth…

Jedrzejewicz showed that a polynomial map over a field of characteristic zero is invertible, if and only if the corresponding endomorphism maps irreducible polynomials to irreducible polynomials. Furthermore, he showed that a polynomial map…

Numerical and theoretical aspects of conformal mappings from a disk to a circular-arc quadrilateral, symmetric with respect to the coordinate axes, are developed. The problem of relating the accessory parameters (prevertices together with…

In this note, we investigate the dynamics of invariant circles in area-preserving twist maps. The invariant circles under consideration lie beyond the applicability of classical KAM theory, as the perturbations involved exceed the scope of…

An element of a group is \emph{reversible} if it is conjugate to its own inverse, and it is \emph{strongly reversible} if it is conjugate to its inverse by an involution. A group element is strongly reversible if and only if it can be…

Because of all the known integrable models possess Schwarzian forms with M\"obious transformation invariance, it may be one of the best way to find new integrable models starting from some suitable M\"obious transformation invariant…

We study a class of one-dimensional full branch maps admitting two indifferent fixed points as well as critical points and/or unbounded derivative. Under some mild assumptions we prove the existence of a unique invariant mixing absolutely…

We consider the existence of invariant curves of real analytic reversible mappings which are quasi-periodic in the angle variables. By the normal form theorem, we prove that under some assumptions, the original mapping is changed into its…

We present an algorithmic equivalent statement to the Jacobian conjecture. Given a polynomial map F on an affine space of dimension n, our algorithm constructs n sequences of polynomials such that F is invertible if and only if the zero…

The paper continues the author's research in the problem of quantitative investigation of basic curvelinear quasiinvariants of quasiconformal curves. It concerns polygons with infinite number of vertices and provides various distortion…