Related papers: Homoclinic classes with shadowing property

For hyperbolic diffeomorphisms, we define adjoint shadowing directions as a bounded inhomogeneous adjoint solution whose initial condition has zero component in the unstable adjoint direction. For hyperbolic flows, we define adjoint…

In this paper, we study one of the fundamental notions in dynamical systems, the shadowing of invertible (bounded and linear) operators on a Hilbert space. Although the problem of finding a spectral characterization for shadowing has been…

An automorphism of a building is called uniclass if the Weyl distance between any chamber and its image lies in a unique (twisted) conjugacy class of the Coxeter group. In a previous paper we characterised uniclass automorphisms of…

In this paper we prove that the homotopy class of non-homothety linear endomorphisms on $\mathbb{T}^2$ with determinant greater than 2 contains a $C^1$ open set of non-uniformly hyperbolic endomorphisms. Furthermore, we prove that the…

We prove that every topological conjugation between two germs of singular holomorphic curves in the complex plane is homotopic to another conjugation which extends homeomorphically to the exceptional divisors of their minimal…

The notion of stochastic shadowing property is introduced. Relations to stochastic stability and standard shadowing are studied. Using tent map as an example it is proved that, in contrast to what happens for standard shadowing, there are…

The aim of this article is twofold: First we study holomorphic germs of parabolic diffeomorphisms of $(\mathbb{C}^2,0)$ that are reversed by a holomorphic reflection and posses an analytic first integral with non-degenerate critical point…

We deal with dynamical systems on complex lattices possessing chains of non-transversal heteroclinic connections between several periodic orbits. The systems we consider are inspired by the so-called \emph{toy model systems} (TMS) used to…

In this article we prove that, restricted to the row-constrained case, effective sets of colourings in the $2$-fold horocyclic tessellations of the hyperbolic plane $\mathbb{H}^2$ are sofic.

If G is a (connected) complex Lie Group and Z is a generalized flag manifold for G, the the open orbits D of a (connected) real form G_0 of G form an interesting class of complex homogeneous spaces, which play an important role in the…

For r at least 3, p at least 2, we classify all actions of the groups Diff^r_c(R) and Diff^r_+(S1) by C^p -diffeomorphisms on the line and on the circle. This is the same as describing all nontrivial group homomorphisms between groups of…

For a class of robustly transitive diffeomorphisms on $\mathbb T^4$ introduced by Shub in [24], satisfying an additional bunching condition, we show that there exits a $C^2$ open and $C^r$ dense subset $\mathcal U^r$, $2\leq r\leq\infty$,…

Following Part~I, we consider a class of reversible systems and study bifurcations of homoclinic orbits to hyperbolic saddle equilibria. Here we concentrate on the case in which homoclinic orbits are symmetric, so that only one control…

Hom-Lie superalgebras can be considered as the deformation of Lie superalgebras; which are $\mathbb{Z}_2$-graded generalization of Hom-Lie algebras. The motivation of this paper is to introduce the concept of isoclinism and factor set in…

The main question we target is the following: If one fixes a topological type of a complex normal surface singularity then what are the possible analytic types supported by it, and/or, what are the possible values of the geometric genus? We…

A cocycle category H(X,Y) is defined for objects X and Y in a model category, and it is shown that the set of morphisms [X,Y] is isomorphic to the set of path components of H(X,Y) provided the ambient model category is right proper and…

We prove that if $f$ is a $C^{1+}$ partially hyperbolic diffeomorphism satisfying certain conditions then there is a $C^1$-open neighborhood $\cA$ of $f$ so that every $g\in \cA\cap \operatorname{Diff}^{1+}(M)$ has a unique equilibrium…

We derive a necessary and sufficient condition for a homeomorphism with the shadowing property to be topologically transitive: to have an invariant subset $A$, dense in the non-wandering set, where the barycenter property holds. To…

Given two automorphisms of a group $G$, one is interested in knowing whether they are conjugate in the automorphism group of $G$, or in the abstract commensurator of $G$, and how these two properties may differ. When $G$ is the fundamental…

We study a class of slow-fast Hamiltonian systems with any finite number of degrees of freedom, but with at least one slow one and two fast ones. At $% \epsilon =0$ the slow dynamics is frozen. We assume that the frozen system (i.e. the…