Related papers: Elementary slopes of plane-wide breakout
The orbit closure of the unfolding of every rational right and isosceles triangle is computed and the asymptotic number of periodic billiard trajectories in these triangles is deduced. This follows by classifying all orbit closures of rank…
A simple geometrical model is presented for the gravity-driven motion of a single particle on a rough inclined surface. Adopting a simple restitution law for the collisions between the particle and the surface, we arrive at a model in which…
We investigate minimal surfaces passing a given curve in $R^{3}$. Using the Frenet frame of a given curve and isothermal parameter, we derive the necessary and sufficient condition for minimal surface. Also we derive the parametric…
We consider 1-equivariant wave maps from \R \times (\R^3 \setminus B) to S^3 where B is a ball centered at 0, and the boundary of B gets mapped to a fixed point on S^3. We show that 1-equivariant maps of degree zero scatter to zero…
We present a simple construction of an ODE on $\mathbb{R}^{n}$ where the vector field is smooth, and finite-time blow-up is equivalent to the halting problem for a universal Turing machine.
We examine the possible trajectories of a classical particle, trapped in a two-dimensional infinite rectangular well, using the Hamilton-Jacobi equation. We observe that three types of trajectories are possible: periodic orbits, open orbits…
A widespread framework for understanding frictional rupture, such as earthquakes along geological faults, invokes an analogy to ordinary cracks. A distinct feature of ordinary cracks is that their near edge fields are characterized by a…
We construct the complete set of orders of growth and we define on it the generalized entropy of a dynamical systems. With this object we provide a framework where we can study the separation of orbits of a map beyond the scope of…
Polygonal billiards exhibit a rich and complex dynamical behavior. In recent years polygonal billiards have attracted great attention due to their application in the understanding of anomalous transport, but also at the fundamental level,…
Given a mapping from a set of players to the leaves of a complete binary tree (called a seeding), a knockout tournament is conducted as follows: every round, every two players with a common parent compete against each other, and the winner…
Conventional quantum field theory is a method for studying structureless elementary particles. Non-elementary particles, on the other hand, are those with internal structure or particles that are made up of elementary constituents like the…
A family of orbiting resonances in molecular scattering is globally described by using a single pole moving in the complex angular momentum plane. The extrapolation of this pole at negative energies gives the location of the bound states.…
A connected graph G with at least two vertices is matching covered if each of its edges lies in a perfect matching. We say that an edge e in a matching covered graph G is removable if G-e is matching covered. A pair {e; f} of edges of a…
We show a somewhat surprising result: if $E$ is a disk in the plane $\mathbb R^2$, then there is a homeomorphism $h:\mathbb R^2\rightarrow\mathbb R^2$ such that, for every $x\in\partial E$, the orbit $O(x, h)$ is bounded, but for every…
We construct a sequence of embedded minimal disks in a ball where the curvatures blow up only at the center. The sequence converges to a limit which is not smooth and not proper.
We investigate global continuation of periodic orbits of a differential equation depending on a parameter, assuming that a closed 1-form satisfying certain properties exists. We begin by extending the global continuation theory of…
In the mathematical framework of a restricted, slightly dissipative spin-orbit model, we prove the existence of periodic orbits for astronomical parameter values corresponding to all satellites of the Solar system observed in exact…
Time-dependent Stark-Zeeman systems describe the motion of an electron attracted by a proton subject to a magnetic and a time-dependent electric field. For instance the study of the dynamics of a gateway around the moon which is subject to…
This study analyzed the scar-like localization in the time-average of a timeevolving wavepacket on the desymmetrized stadium billiard. When a wavepacket is launched along the orbits, it emerges on classical unstable periodic orbits as a…
The Drude-Lorentz model for the motion of electrons in a solid is a classical model in statistical mechanics, where electrons are represented as point particles bouncing on a fixed system of obstacles (the atoms in the solid). Under some…