Related papers: Invariant manifolds for the hyperbolic type integr…
In the article we discuss the notion of the generalized invariant manifold introduced in our previous study. In the literature the method of the differential constraints is well known as a tool for constructing particular solutions for the…
Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…
We construct a hyperbolic three-manifold with trivial finite type invariants up to a given degree.
A notion of the generalized invariant manifold for a nonlinear integrable lattice is considered. Earlier it has been observed that this kind objects provide an effective tool for evaluating the recursion operators and Lax pairs. In this…
We prove the meromorphy of solutions for a wide class of ordinary differential equations. These equations are given by invariant manifolds of non-linear partial differential equations integrable by the inverse scattering method. Some higher…
Invariants of general linear system of two hyperbolic partial differential equations (PDEs) are derived under transformations of the dependent and independent variables by real infinitesimal method earlier. Here a subclass of the general…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
Integral invariants obtained from Principal Component Analysis on a small kernel domain of a submanifold encode important geometric information classically defined in differential-geometric terms. We generalize to hypersurfaces in any…
We investigate the existence and regularity of locally invariant manifolds near an approximately invariant set that satisfies a geometric hyperbolicity condition with respect to an abstract ``generalized" dynamical system in Banach spaces.…
The paper gives a comprehensive study of Inertial Manifolds for hyperbolic relaxations of an abstract semilinear parabolic equation in a Hilbert space. A new scheme of constructing Inertial Manifolds for such type of problems is suggested…
In the article differential-difference (semi-discrete) lattices of hyperbolic type are investigated from the integrability viewpoint. More precisely we concentrate on a method for constructing generalized symmetries. This kind integrable…
We show that the standard method for constructing closed hyperbolic manifolds of arbitrary dimension possessing reflective symmetries typically produces reflections whose fixed point sets are nonseparating.
In this paper we study the existence and regularity of stable manifolds associated to fixed points of parabolic type in the differentiable and analytic cases, using the parametrization method. The parametrization method relies on a suitable…
Let $M = G/H$ be an $(n+1)$-dimensional homogeneous manifold and $J^k(n,M)=:J^k$ be the manifold of $k$-jets of hypersurfaces of $M$. The Lie group $G$ acts naturally on each $J^k$. A $G$-invariant PDE of order $k$ for hypersurfaces of $M$…
The aim of this paper is to prove the existence and smoothness of stable and unstable invariant manifolds for a stochastic delayed partial differential equation of parabolic type. The stochastic delayed partial differential equation is…
We present a construction of a large class of Laplace invariants for linear hyperbolic partial differential operators of fairly general form and arbitrary order.
We develop a general framework for numerically solving differential equations while preserving invariants. As in standard projection methods, we project an arbitrary base integrator onto an invariant-preserving manifold, however, our method…
A multi-cube method is developed for solving systems of elliptic and hyperbolic partial differential equations numerically on manifolds with arbitrary spatial topologies. It is shown that any three-dimensional manifold can be represented as…
We consider the generalization of Laplace invariants to linear differential systems of arbitrary rank and dimension. We discuss completeness of certain subsets of invariants.
In this paper we introduce a general type of differential equations with piecewise constant argument (EPCAG), and consider the problem of backward continuation of solutions. We establish the existence of global integral manifolds of…