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  • 1
    Online Resource
    Online Resource
    Amsterdam : North Holland
    Keywords: MATHEMATICS Differential Equations ; General ; Differential equations ; MATHEMATICS / Differential Equations / General / bisacsh
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (1 online resource (xv, 702 p.))
    ISBN: 9780444530318 , 0444530312 , 9780080559469 , 0080559468 , 0444530363 , 9780444530363
    DDC: 515.35
    Language: English
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  • 2
    Online Resource
    Online Resource
    Amsterdam [u.a.] : Elsevier
    Part of " Handbook of differential equations"
    Keywords: Gewöhnliche Differentialgleichung ; Differential equations ; Gewöhnliche Differentialgleichung
    Abstract: This handbook is the fourth volume in a series of volumes devoted to self contained and up-to-date surveys in the theory of ordinary differential equations, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience. * Covers a variety of problems in ordinary differential equations * Pure mathematical and real world applications * Written for mathematicians and scientists of many related fields
    Type of Medium: Online Resource
    Pages: 1 Online-Ressource (xv, 702 Seiten)
    ISBN: 0444530312 , 9780444530318
    URL: Volltext  (URL des Erstveröffentlichers)
    DDC: 515.35
    RVK:
    Language: English
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1420-9004
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The problem of existence of aglobal center manifold for a system of O.D.E. like (*) $$\left\{ {\begin{array}{*{20}c} {\dot x = A(y)x + F(x,y)} \\ {\dot y = G(x,y), (x,y) \in \mathbb{R}^n \times \mathbb{R}^m ,} \\ \end{array} } \right.$$ is considered. We give conditions onA(y), F(x, y), G(x, y) in order that a functionH: ℝ m →ℝ n , with the same smoothness asA(y), F(x, y), G(x, y), exists and is such that the manifoldC={(x,y)∈ℝ n ×ℝ m ∣x=H(y),y∈ℝ m } is an invariant manifold for (*), and there exists ρ〉0 such that any solution of (*) satisfying sup t∈ℝ∣x(t)∣ 〈ρ must belong toC. This is why we callC global center manifold. Applications are given to the problem of existence of heteroclinic orbits in singular systems.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider the problem of bifurcation as well as of accumulation of periodic orbits on heteroclinic orbits for certain systems of ordinary differential equations either equivariant under finite groups of linear transformations or periodic in spatial variables.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Annali di matematica pura ed applicata 166 (1994), S. 267-289 
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We study the problem of bifurcation from a heteroclinic orbit joining two semi-hyperbolic equilibrium points E1 and E2. We show that, if certain non-degeneracy assumptions are satisfied, E1 and E2 split into two equilibria Eij, i,j= 1,2, and there are Melnikov-type conditions assuring the existence of a heteroclinic orbit from E1i to E2j, i,j=1,2 along directions that are tangent to the strongly-unstable (resp. strongly-stable) manifold of E1j (resp. E2j.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Annali di matematica pura ed applicata 151 (1988), S. 369-387 
    ISSN: 1618-1891
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Sunto Viene presentato un nuovo metodo per la determinazione degli sviluppi asintotici della soluzione esterna di sistemi di equazioni differenziali ordinarie singolarmente perturbati. Il metodo proposto, basato sulla teoria geometrica delle perturbazioni singolari e in particolare su un teorema di esistenza di varietà centrale, permette di ottenere le equazioni differenziali che definiscono le variabili « lente » senza la preventiva conoscenza dei corrispondenti sviluppi per le variabili « veloci ». Inoltre, se i sistemi vengono dati con condizioni iniziali, alcune formule che esprimono le corrette condizioni iniziali da assegnare alle equazioni differenziali trovate — formule già note nel « caso stabile » — vengono estese al « caso condizionalmente stabile »; il procedimento qui usato risulta anche più sintetico rispetto a quelli precedentemente proposti. Infine viene studiata un'applicazione ad una classe assai generale di equazioni derivanti dalla cinetica delle reazioni enzimatiche.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1572-9222
    Keywords: Exponential dichotomies ; heteroclinic orbits ; singular perturbations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider singularly perturbed systems $$\xi = f(\xi ,\eta ,\varepsilon ),\dot \eta = \varepsilon g(\xi ,\eta ,\varepsilon )$$ , such thatξ=f(ξ, αo, 0). αo∃ℝ m , has a heteroclinic orbitu(t). We construct a bifurcation functionG(α, ɛ) such that the singular system has a heteroclinic orbit if and only ifG(α, ɛ)=0 has a solutionα=α(ɛ). We also apply this result to recover some theorems that have been proved using different approaches.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1572-9222
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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