Related papers: Critical set for surface diffeomorphisms revisited
We show that the identity component of the group of diffeomorphisms of a closed oriented surface of positive genus admits many unbounded quasi-morphisms. As a corollary, we also deduce that this group is not uniformly perfect and its…
After a brief review of the historical role of analyticity in the study of critical phenomena, an account is given of recent discoveries of discretely holomorphic observables in critical two-dimensional lattice models. These are objects…
Critical surfaces are defined by Bachman as topological index 2 surfaces, generalizing incompressible surfaces and strongly irreducible surfaces. In this paper we give a condition to obtain critical Heegaard surfaces by amalgamation. As a…
We provide a complete system of invariants for the formal classification of complex analytic unipotent germs of diffeomorphism at $\cn{n}$ fixing the orbits of a regular vector field. We reduce the formal classification problem to solve a…
We study the existence of points on a compact oriented surface at which a symmetric bilinear two-tensor field is conformal to a Riemannian metric. We give applications to the existence of conformal points of surface diffeomorphisms and…
We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…
The main result of this paper is that every non-trivial Hamiltonian diffeomorphism of a closed oriented surface of genus at least one has periodic points of arbitrarily high period. The same result is true for S^2 provided the…
This paper is a step towards the complete topological classification of {\Omega}-stable diffeomorphisms on an orientable closed surface, aiming to give necessary and sufficient conditions for two such diffeomorphisms to be topologically…
We use symplectic tools to establish a smooth variant of Franks theorem for a closed orientable surface of positive genus $g$; it implies that a symplectic diffeomorphism isotopic to the identity with more than $2g-2$ fixed points, counted…
We discuss dynamics of skew product maps defined by circle diffeomorphisms forced by expanding circle maps. We construct an open class of such systems that are robust topologically mixing and for which almost all points in the same fiber…
Given a two--dimensional mapping $U$ whose components solve a divergence structure elliptic equation, we give necessary and sufficient conditions on the boundary so that $U$ is a global diffeomorphism.
We consider critical curves -- conformally invariant curves that appear at critical points of two-dimensional statistical mechanical systems. We show how to describe these curves in terms of the Coulomb gas formalism of conformal field…
In this paper, a new kind of soft sets related with some common decision making problems in real life called central soft sets is introduced. Properties of some basic operations on central soft sets are shown. It is investigated that some…
We classify all ruled surfaces in Euclidean space that are critical points of the Dirichlet energy, obtaining explicit parametrizations of these surfaces.
A classical result due to Blaschke states that for every analytic self-map $f$ of the open unit disk of the complex plane there exists a Blaschke product $B$ such that the zero sets of $f$ and $B$ agree. In this paper we show that there is…
For any compact, connected, orientable, finite-type surface with marked points other than the sphere with three marked points, we construct a finite rigid set of its arc complex: a finite simplicial subcomplex of its arc complex such that…
We exhibit a local residual set of surface $C^1$ diffeomorphisms that are continuum-wise expansive but are not expansive. We also exhibit an open and dense set of surface $C^1$ diffeomorphisms where expansiveness implies being Anosov.
We describe dimensional entropies introduced in a previous work list some of their properties and give some new proofs. These entropies allowed the definition of entropy-expanding maps. We introduce a new notion of entropy-hyperbolicity for…
We extend Choe's idea in \cite{choe} to nonpolyhedral calibrated surfaces and give some examples of polyhedral sets over right prisms and nonpolyhedral calibrated surfaces.
I study the two-dimensional defects of the $d$ dimensional critical $O(N)$ model and the defect RG flows between them. By combining the $\epsilon$-expansion around $d = 4$ and $d = 6$ as well as large $N$ techniques, I find new conformal…