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  • 1
    Electronic Resource
    Electronic Resource
    Center manifold and stability for skew-product flows (1994)
    Springer
    Journal of dynamics and differential equations 6 (1994), S. 543-582 
    Details
    ISSN: 1572-9222
    Keywords: Center-like manifolds ; invariant foliations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study the existence and smoothness of global center, center-stable, and center-unstable manifolds for skew-product flows. Smooth invariant foliations to the center stable and center unstable manifolds are also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02218847
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Homoclinic bifurcation at resonant eigenvalues (1990)
    Springer
    Journal of dynamics and differential equations 2 (1990), S. 177-244 
    Details
    ISSN: 1572-9222
    Keywords: homoclinic orbit ; period doubling ; pathfollowing ; global bifurcation ; resonance ; 34C15 ; 34C35 ; 58F14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a bifurcation of homoclinic orbits, which is an analogue of period doubling in the limit of infinite period. This bifurcation can occur in generic two parameter vector fields when a homoclinic orbit is attached to a stationary point with resonant eigenvalues. The resonance condition requires the eigenvalues with positive/negative real part closest to zero to be real, simple, and equidistant to zero. Under an additional global twist condition, an exponentially flat bifurcation of double homoclinic orbits from the primary homoclinic branch is established rigorously. Moreover, associated period doublings of periodic orbits with almost infinite period are detected. If the global twist condition is violated, a resonant side switching occurs. This corresponds to an exponentially flat bifurcation of periodic saddle-node orbits from the homoclinic branch.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01057418
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    On the numerical computation of orbits of dynamical systems: The one-dimensional case (1991)
    Springer
    Journal of dynamics and differential equations 3 (1991), S. 361-379 
    Details
    ISSN: 1572-9222
    Keywords: Dynamical systems ; numerically computed orbits ; shadowing ; pseudo-orbits ; round-off ; expansiveness
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A finite time version of the shadowing theorem is used to develop a procedure to determine the accuracy of numerically computed orbits of one-dimensional maps. The procedure works forward. After any given number of iterates, we can decide whether our theorem applies and, if it does, we can estimate how far the computed orbit is from a true orbit.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01049737
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    Paper (German National Licenses)
    Fulltext
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