Results 91 to 100 of about 363,931 (208)
Center manifolds and contractions on a scale of Banach spaces
Journal of Functional Analysis, 1987 The paper contains a new proof of the existence of a \(C^ k\)-center manifold at a nonhyperbolic equilibrium point of a finite-dimensional vectorfield of class \(C^ k\). The main idea is that (after an appropriate globalization of the problem) such center manifold contains all solutions which have a certain maximal exponential growth at infinity.
S. A. van Gils, André Vanderbauwhede
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Construction of blow‐up solutions for Liouville systems
Proceedings of the London Mathematical Society, Volume 131, Issue 4, October 2025.Abstract We study the following Liouville system defined on a flat torus −Δui=∑j=1naijρjhjeuj∫Ωhjeuj−1,uj∈Hper1(Ω)fori∈I={1,…,n},$$\begin{equation*} {\left\lbrace \def\eqcellsep{&}\begin{array}{lr}-\Delta u_i=\sum _{j=1}^n a_{ij}\rho _j{\left(\frac{h_j e^{u_j}}{\int _\Omega h_j e^{u_j}}-1\right)},\\[3pt] u_j\in H_{per}^1(\Omega)\mbox{ for }i\in I ...
Zetao Cheng, Haoyu Li, Lei Zhang
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Generic transitivity for couples of Hamiltonians
, 2013 We study orbits and reachable sets of generic couples of Hamiltonians $H_1, H_2$ on a symplectic manifold $N$. We prove that, $C^k$-generically for $k$ large enough, orbits coincide with the whole of $N$, and that the same is true for reachable sets when
Mandorino, Vito
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Mathematical Methods in the Applied Sciences, Volume 48, Issue 14, Page 13456-13474, 30 September 2025.ABSTRACT We present sufficient conditions to obtain a generalized (φ,D)$$ \left(\varphi, \mathfrak{D}\right) $$‐pullback attractor for evolution processes on time‐dependent phase spaces, where φ$$ \varphi $$ is a given decay function and D$$ \mathfrak{D} $$ is a given universe.
Matheus Cheque Bortolan +3 more
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Existence of conjugacies and stable manifolds via suspensions
Electronic Journal of Differential Equations, 2017 We obtain in a simpler manner versions of the Grobman-Hartman theorem and of the stable manifold theorem for a sequence of maps on a Banach space, which corresponds to consider a nonautonomous dynamics with discrete time.
Luis Barreira +2 more
doaj
Attractors for an Energy‐Damped Viscoelastic Plate Equation
Mathematical Methods in the Applied Sciences, Volume 48, Issue 14, Page 13864-13881, 30 September 2025.ABSTRACT In this paper, we consider a class of non‐autonomous beam/plate equations with an integro‐differential damping given by a possibly degenerate memory and an energy damping given by a nonlocal ε$$ \varepsilon $$‐perturbed coefficient. For each ε>0$$ \varepsilon >0 $$, we show that the dynamical system generated by the weak solutions of the ...
V. Narciso +3 more
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Algebraic characterization of symmetric complex Banach manifolds [PDF]
Mathematische Annalen, 1977 The symmetric hermitian complex manifolds (of finite dimension) have been classi fled completely by E. Cartan [4] using the classification of simple complex Lie algebras. A Jordan theoretic approach is due to Koecher [18] and more recently to Loos [25] : The symmetric bounded domains are in a one-to-one correspondence to hermitian Jordan triple systems,
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First‐order Sobolev spaces, self‐similar energies and energy measures on the Sierpiński carpet
Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1523-1608, September 2025.Abstract For any p∈(1,∞)$p \in (1,\infty)$, we construct p$p$‐energies and the corresponding p$p$‐energy measures on the Sierpiński carpet. A salient feature of our Sobolev space is the self‐similarity of energy. An important motivation for the construction of self‐similar energy and energy measures is to determine whether or not the Ahlfors regular ...
Mathav Murugan, Ryosuke Shimizu
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Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1783-1842, September 2025.Abstract We consider the global dynamics of finite energy solutions to energy‐critical equivariant harmonic map heat flow (HMHF) and radial nonlinear heat equation (NLH). It is known that any finite energy equivariant solutions to (HMHF) decompose into finitely many harmonic maps (bubbles) separated by scales and a body map, as approaching to the ...
Kihyun Kim, Frank Merle
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Tame Fr\'echet submanifolds [PDF]
, 2013 We introduce the new class of submanifolds of co-Banach type in tame Fr\'echet manifolds and construct tame Fr\'echet submanifolds as inverse images of regular values of certain tame maps.
Freyn, Walter
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