Related papers: Backward orbits in the unit ball
Assuming some regularity of the dynamical zeta function, we establish an explicit formula with an error term for the prime orbit counting function of a suspended flow. We define the subclass of self-similar flows, for which we give an…
We consider the Dirichlet-to-Neumann map $\Lambda$ on a cylinder-like Lorentzian manifold related to the wave equation related to the metric $g$, a magnetic field $A$ and a potential $q$. We show that we can recover the jet of $g,A,q$ on…
We establish an analogue of Ratner's orbit closure theorem for any connected closed subgroup generated by unipotent elements in $\operatorname{SO}(d,1)$ acting on the space $\Gamma\backslash \operatorname{SO}(d,1)$, assuming that the…
We prove that if $G\subset\text{Diff}^{1}(\mathbb{R}^2)$ is an Abelian subgroup generated by a family of commuting diffeomorphisms of the plane, all of which are $C^{1}$-close to the identity in the strong $C^{1}$-topology, and if there…
We consider a homoclinic orbit to a saddle fixed point of an arbitrary $C^\infty$ map $f$ on $\mathbb{R}^2$ and study the phenomenon that $f$ has an infinite family of asymptotically stable, single-round periodic solutions. From classical…
A tuple (or subgroup) in a group is said to degenerate to another if the latter is an endomorphic image of the former. In a countable reduced abelian group, it is shown that if tuples (or finite subgroups) degenerate to each other, then…
Vertex models with quantum group symmetry give rise to integrable cellular automata at q=0. We study a prototype example known as the periodic box-ball system. The initial value problem is solved in terms of an ultradiscrete analogue of the…
Motivated by the study of periods of automorphic forms and relative trace formulae, we develop the theory of descent necessary to study orbital integrals arising in the fundamental lemma for a general class of symmetric spaces over a…
The aim of this paper is to study global bifurcations of non-constant solutions of some nonlinear elliptic systems, namely the system on a sphere and the Neumann problem on a ball. We study the bifurcation phenomenon from families of…
This paper considers a class of delay differential equations with unimodal feedback and describes the structure of certain unstable sets of stationary points and periodic orbits. These unstable sets consist of heteroclinic connections from…
Consider the semilinear elliptic equation $-\Delta u=\lambda f(u)$ in the unit ball $B_1\subset \mathbb{R}^N$, with Dirichlet data $u|_{\partial B_1}=0$, where $\lambda\geq 0$ is a real parameter and $f$ is a $C^1$ positive, nondecreasing…
In this paper, we explore the local geometry of dynamical systems $\dot{x}=F(x)$ with real time parameterization, where $F$ is holomorphic on connected open subsets of $\mathbb{C}\stackrel{\sim}{=}\mathbb{R}^2$. We describe the geometry of…
The model of a bicycle is a unit segment AB that can move in the plane so that it remains tangent to the trajectory of point A (the rear wheel is fixed on the bicycle frame); the same model describes the hatchet planimeter. The trajectory…
We consider the following conjecture (from Huang, et al): Let $\Delta^+$ denote the upper half disc in $\mathbb{C}$ and let $\gamma = ( - 1, 1)$ (viewed as an interval in the real axis in $\mathbb{C}$). Assume that $F$ is a holomorphic…
In this paper, we prove that fractal zeta functions of orbits of parabolic germs of diffeomorphisms can be meromorphically extended to the whole complex plane. We describe their set of poles (i.e. their complex dimensions) and their…
The collapse of a vapor bubble near a flat solid boundary results in the formation of a jet that is directed towards the boundary. In more complex geometries such as corners, predictions of the collapse cannot be made in a straightforward…
Let $-1<\lambda<1$ and $f:[0,1)\to\mathbb{R}$ be a piecewise $\lambda$-affine map, that is, there exist points $0=c_0<c_1<\cdots <c_{n-1}<c_n=1$ and real numbers $b_1,\ldots,b_n$ such that $f(x)=\lambda x+b_i$ for every $x\in…
We introduce and study a non uniform hyperbolicity condition for complex rational maps, that does not involve a growth condition. We call this condition Backward Contraction. We show this condition is weaker than the Collet-Eckmann…
In this note we analyze how perturbations of a ball $\mathfrak{B}_r \subset \mathbb{R}^n$ behaves in terms of their first (non-trivial) Neumann and Dirichlet $\infty-$eigenvalues when a volume constraint $\\mathscr{L}^n(\Omega) =…
Bernoulli convolutions are certain measures on the unit interval depending on a parameter $\beta$ between 1 and 2. In spite of their simple definition, they are not yet well understood. We study their two-dimensional density which exists by…