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Invariant Algebraic Manifolds for the Rucklidge Model of Double Convection
Invariant manifolds are important for describing the dynamics of systems of ODEs. In this article we classify invariant algebraic manifolds in the...
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Data-Driven Reduced Order Models Using Invariant Foliations, Manifolds and Autoencoders
This paper explores how to identify a reduced order model (ROM) from a physical system. A ROM captures an invariant subset of the observed dynamics....
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Conformal Anti-Invariant Riemannian Maps from or To Sasakian Manifolds
AbstractIn this article, we introduce conformal anti-invariant Riemannian maps from or to Sasakian manifolds to or from Riemannian manifolds. We...
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Invariant Manifolds for a PDE-ODE Coupled System
The aim of this paper is to construct invariant manifolds for a coupled system, consisting of a parabolic equation and a second-order ordinary...
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Left-invariant almost complex structures on the higher dimensional Kodaira–Thurston manifolds
We develop computational techniques which allow us to calculate the Kodaira dimension as well as the dimension of spaces of Dolbeault harmonic forms...
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The 3-D Nonlinear Hyperbolic–Parabolic Problems: Invariant Manifolds
We investigate the existence of invariant manifolds for a coupled problem of nonlinear hyperbolic–parabolic PDEs on a 3-D torus. The problem arises...
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Invariant Manifolds. Global Attractor of a Generalized Version of the Nonlocal Ginzburg–Landau Equation
We consider a generalized nonlocal Ginzburg–Landau equation with periodic boundary conditions. For the corresponding initial-boundary value problem...
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Finite element approximation of invariant manifolds by the parameterization method
We combine the parameterization method for invariant manifolds with the finite element method for elliptic PDEs, to obtain a new computational...
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Local Bifurcations of Invariant Manifolds of the Cahn–Hilliard–Oono Equation
AbstractOur aim is to examine a periodic boundary value problem for the Cahn–Hilliard–Oono equation. This equation appeared as one of the possible...
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Scalar Curvatures of Invariant Almost Hermitian Structures on Flag Manifolds with Two and Three Isotropy Summands
In this paper, we study invariant almost Hermitian geometry on generalized flag manifolds which the isotropy representation decompose into two or...
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Invariant Forms of Geodesic, Potential, and Dissipative Systems on Tangent Bundles of Finite-Dimensional Manifolds
AbstractIt is well known [1–3] that a system of differential equations can be exactly integrated if a sufficient number of its tensor invariants (not...
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Equivalence of invariant metrics via Bergman kernel on complete noncompact Kähler manifolds
We study equivalence of invariant metrics on noncompact Kähler manifolds with a complete Bergman metric of bounded curvature. Especially only the...
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Clairaut Semi-invariant Riemannian Maps to Kähler Manifolds
In this paper, first, we recall the notion of Clairaut Riemannian map (CRM) F using a geodesic curve on the base manifold and give the Ricci...
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Nonlinear Model Reduction for Slow–Fast Stochastic Systems Near Unknown Invariant Manifolds
We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant...
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Contact Manifolds
In the study of geometric aspects of classical mechanics, besides symplectic manifolds that are even dimensional, there are contact manifolds that...