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We present a new approach to the problem of proving global stability, based on symplectic geometry and with a focus on systems with several conserved quantities. We also provide a proof of instability for integrable systems whose momentum…
We present a new approach for predicting stable equilibrium shapes of crystalline islands on flat substrates, as commonly occur through solid-state dewetting of thin films. The new theory is a generalization of the widely used Winterbottom…
In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the linear wave…
Single-loop elastic rings can be folded into multi-loop equilibrium configurations. In this paper, the stability of several such multi-loop states which are either circular or straight are investigated analytically and illustrated by…
The equilibrium configuration of an engineering structure, able to withstand a certain loading condition, is usually associated with a local minimum of the underlying potential energy. However, in the nonlinear context, there may be other…
Within the context of modified gravity and dark energy scenarios of the accelerating universe, we study the stability of de Sitter space with respect to inhomogeneous perturbations using a gauge-independent formalism. In modified gravity…
Lie groupoids generalize transformation groups, and so provide a natural language for studying orbifolds and other noncommutative geometries. In this paper, we investigate a connection between orbifolds and equivariant stable homotopy…
We prove the linear orbital stability of spectrally stable stationary discrete shock profiles for conservative finite difference schemes applied to systems of conservation laws. The proof relies on an accurate description of the pointwise…
Peixoto's structural stability and density theorems represent milestones in the modern theory of dynamical systems and their applications. Despite the importance of these theorems, they are often treated rather superficially, if at all, in…
The problem of homological stability helps us to catch the structure of group homology. We calculate homological stability of special orthogonal groups, and we also calculate the stability of orthogonal groups with determinant-twisted…
Designing for rotational stability can dramatically affect the geometry of a space station. If improperly designed, the rotating station could end up catastrophically tumbling end-over-end. Active stabilization can address this problem;…
The Ward equation, also called the modified 2+1 chiral model, is obtained by a dimension reduction and a gauge fixing from the self-dual Yang-Mills field equation on $R^{2,2}$. It has a Lax pair and is an integrable system. Ward constructed…
The aim of this work is to establish a instability study for stationary kink and antikink/kink profiles solutions for the sine-Gordon equation on a metric graph with a structure represented by a Y-junction so-called a Josephson tricrystal…
The study of circular orbits in spacetime is of astrophysical importance. The identification and classification of circular orbits in both static and stationary spacetimes remains an active area of interest. Even in the simplest static…
In this manuscript we consider the stability of periodic solutions to Lambda-Omega lattice dynamical systems. In particular, we show that an appropriate ansatz casts the lattice dynamical system as an infinite-dimensional fast-slow…
We survey recent work that relates Pitman's transformation to a variety of classical integrable systems, including the box-ball system, the ultra-discrete and discrete KdV equations, and the ultra-discrete and discrete Toda lattice…
We construct and simulate the dynamics of gauged vortons - circular loops of cosmic string supported by the angular momentum of trapped charge and current and provide additional details on the fully stable vorton that we have previously…
B\"acklund transformations (BTs) are traditionally regarded as a tool for integrating nonlinear partial differential equations (PDEs). Their use has been recently extended, however, to problems such as the construction of recursion…
Birkhoff normal forms are commonly used in order to ensure the so called "effective stability" in the neighborhood of elliptic equilibrium points for Hamiltonian systems. From a theoretical point of view, this means that the eventual…
We consider the Taylor-Couette problem in an infinitely extended cylindrical domain. There exist modulated front solutions which describe the spreading of the stable Taylor vortices into the region of the unstable Couette flow. These…