Related papers: In search of stable geometric structures
Understanding which system structure can sustain stable dynamics is a fundamental step in the design and analysis of large scale dynamical systems. Towards this goal, we investigate here the structural stability of systems with a random…
Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific sub-class of…
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…
An input-output approach to stability analysis is explored for networked systems with uncertain link dynamics. The main result consists of a collection of integral quadratic constraints, which together imply robust stability of the…
These lectures present results and problems on the characterization of structurally stable dynamics. We will shed light those which do not seem to depend on the regularity class (holomorphic or differentiable). Furthermore, we will present…
Let $M$ be a $10$-dimensional closed oriented smooth manifold. Set $$\mathcal{D}_{M} := \{ x \in H^{2}(M; \Z/2) \mid x^{2} + w_{2}(M) x \in \rho_{2} ( TH^{4}(M;\Z) ) \}.$$ Suppose that $H_{1}(M;\Z)=0$ and $\mathcal{D}_{M} \subset \rho_{2}(…
In this paper, we investigate stable matching in structured networks. Consider case of matching in social networks where candidates are not fully connected. A candidate on one side of the market gets acquaintance with which one on the…
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;…
We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…
We investigate the stability of the holographic description of the universe. By treating the perturbation globally, we discover that this description is stable, which is support for the holographic description of the universe.
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
This note presents a summary and review of various conditions and characterizations for matrix stability (in particular diagonal matrix stability) and matrix stabilizability.
We prove a strong non-structure theorem for a class of metric structures with an unstable pair of formulae. As a consequence, we show that weak categoricity (that is, categoricity up to isomorphisms and not isometries) implies several…
We discuss the stability of three- and four-particle system interacting by pure Coulomb interactions, as a function of the masses and charges of the particles. We present a certain number of general properties which allow to answer a…
The issues of robust stability for two types of uncertain fractional-order systems of order $\alpha \in (0,1)$ are dealt with in this paper. For the polytope-type uncertainty case, a less conservative sufficient condition of robust…
The constraints on the models for the structure formation arising from various cosmological observations at different length scales are reviewed. The status of different models for structure formation is examined critically in the light of…
We study stability patterns in the high dimensional rational homology of unordered configuration spaces of manifolds. Our results follow from a general approach to stability phenomena in the homology of Lie algebras, which may be of…
We develop several aspects of local and global stability in continuous first order logic. In particular, we study type-definable groups and genericity.
In four-dimensional symplectic maps complex instability of periodic orbits is possible, which cannot occur in the two-dimensional case. We investigate the transition from stable to complex unstable dynamics of a fixed point under parameter…
We study the notion of geometric structures for toposes: This generalizes the notion of (X,G) manifolds. We give some applications to algebraic geometry