Related papers: In search of stable geometric structures
The construction of gauge-invariant variables for any order perturbations is discussed. Explicit constructions of the gauge-invariant variables for perturbations to 4th order are shown. From these explicit construction, the recursive…
We survey stability properties of several families of moduli spaces, with a focus on braid groups and configuration spaces.
This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system Hamiltonian. Some general stability results are given for different classes of perturbations to the…
Recently, a classical approach to continuous structures has been proposed in [ABBMZ] and [Z] that extends the class of structures falling under the scope of [HI] or [BBHU]. These articles introduce the notion of structures with a standard…
A stable generalized complex structure is one that is generically symplectic but degenerates along a real codimension two submanifold, where it defines a generalized Calabi-Yau structure. We introduce a Lie algebroid which allows us to view…
This is a survey on the local structure about a fixed point of discrete finite-dimensional holomorphic dynamical systems, discussing in particular the existence of local topological conjugacies to normal forms, and the structure of local…
We present a novel geometric approach for determining the unique structure of a Hamiltonian and establishing an instability criterion for quantum quadratic systems. Our geometric criterion provides insights into the underlying geometric…
The 2-sets convex feasibility problem aims at finding a point in the intersection of two closed convex sets $A$ and $B$ in a normed space $X$. More generally, we can consider the problem of finding (if possible) two points in $A$ and $B$,…
We analyze properties of unstable systems at rest and in motion.
We construct infinite families of topologically isotopic but smoothly distinct knotted spheres in many simply connected 4-manifolds that become smoothly isotopic after stabilizing by connected summing with $S^2 \times S^2$, and as a…
We describe stability conditions for pairs consisting of a coherent sheaf and a homomorphism to a fixed coherent sheaf on a projective variety. The corresponding moduli spaces are constructed for pairs on curves and surfaces. We consider…
This is a brief review of recent theoretical efforts to understand persistence in nonequilibrium systems. Some of the recent experimental results are also briefly mentioned. I also discuss recent generalizations of persistence in various…
We investigate the presence of localized solutions in models described by a single real scalar field with generalized dynamics. The study offers a method to solve very intricate nonlinear ordinary differential equations, and we illustrate…
Necessary and sufficient conditions for the internal stability of formations whose dynamics are obtained is determined by linear differential equations.
We establish various stability results for symplectic surfaces in symplectic $4-$manifolds with $b^+=1$. These results are then applied to prove the existence of representatives of Lagrangian ADE-configurations as well as to classify…
On objects of a triangulated category with a stability condition, we construct a topology.
We survey some aspects of stability conditions both in general and on the derived category of coherent sheaves on a surface, with applications to the birational geometry of certain holomorphic symplectic varieties.
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
With the rise of network science old topics in ecology and economics are resurfacing. One such topic is structural stability (often referred to as qualitative stability or sign stability). A system is deemed structurally stable if the…
Context: Numerous theoretical studies of the stellar dynamics of triple systems have been carried out, but fewer purely empirical studies that have addressed planetary orbits within these systems. Most of these empirical studies have been…