Related papers: Holomorphic slow-fast systems

In this paper, we study transitive partially hyperbolic diffeomorphisms with one-dimensional topologically neutral center, meaning that the length of the iterate of small center segments remains small. Such systems are dynamically coherent.…

We show that nonrelativsitic scaling of the collisionless Vlasov-Maxwell system implies the existence of a formal invariant slow manifold in the infinite-dimensional Vlasov-Maxwell phase space. Vlasov-Maxwell dynamics restricted to the slow…

We consider a dynamical system which has the hyperbolic structure along an attracting invariant manifold $M$. The problem is whether every motion starting in a neighborhood of $M$ possesses an asymptotic phase, i.e. eventually approaches a…

Consider a complex one dimensional foliation on a complex surface near a singularity $p$. If $\mathcal{I}$ is a closed invariant set containing the singularity $p$, then $\mathcal{I}$ contains either a separatrix at $p$ or an invariant real…

We study the compactness problem for moduli spaces of holomorphic supercurves which, being motivated by supergeometry, are perturbed such as to allow for transversality. We give an explicit construction of limiting objects for sequences of…

Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given…

The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…

Invariant manifolds facilitate the understanding of nonlinear stochastic dynamics. When an invariant manifold is represented approximately by a graph for example, the whole stochastic dynamical system may be reduced or restricted to this…

We consider a discrete dynamical system on a pseudo-Riemannian manifold and we determine the concept of a hyperbolic set for it. We insert a condition in the definition of a hyperbolic set which implies to the unique decomposition of a part…

We investigate the realisability of the Casson-Sullivan invariant for homeomorphisms of smooth $4$-manifolds, which is the obstruction to a homeomorphism being stably pseudo-isotopic to a diffeomorphism, valued in the third cohomology of…

We extensively investigate two-step shape invariance in the framework of N-fold supersymmetry. We first show that any two-step shape-invariant system possesses type A 2-fold supersymmetry with an intermediate Hamiltonian and thus has…

Spectral submanifolds (SSMs) are invariant manifolds of a dynamical system, defined by the property of being tangent to a spectral subspace of the linearized dynamics at a steady state. We show existence, along with certain desirable…

The symmetries of two-dimensional supersymmetric sigma models on target spaces with covariantly constant forms associated to special holonomy groups are analysed. It is shown that each pair of such forms gives rise to a new one, called a…

Finite-order invariants of knots in arbitrary 3-manifolds (including non-orientable ones) are constructed and studied by methods of the topology of discriminant sets. Obstructions to the integrability of admissible weight systems to…

We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear difference equations assuming a very general form of dichotomic behavior for the linear equation. The results obtained…

Let $M$ be a hyperkaehler manifold, and $F$ a torsion-free and reflexive coherent sheaf on $M$. Assume that $F$ (outside of its singularities) admits a connection with a curvature which is invariant under the standard SU(2)-action on…

On a compact K\"{a}hler manifold $X$ with a holomorphic 2-form $\a$, there is an almost complex structure associated with $\a$. We show how this implies vanishing theorems for the Gromov-Witten invariants of $X$. This extends the approach,…

We study the problem of persistence of attractors with smooth boundary for a class of set-valued dynamical systems that naturally arise in the context of random and control dynamical systems, as well as in systems modeling the dynamical…

For a class of $(N+1)$-dimensional systems of differential delay equations with a cyclic and monotone negative feedback structure, we construct a two-dimensional invariant manifold, on which phase curves spiral outward towards a bounding…

The stability of the system is an important part of the research on differential dynamical systems. This paper considers a pointwise hyperbolic system defined on a connected open subset N of a compact smooth Riemannian manifold M. The…