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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of dynamics and differential equations 4 (1992), S. 95-126 
    ISSN: 1572-9222
    Keywords: Homoclinic orbit ; bifurcation ; reversible ; Hamiltonian ; saddle-center ; periodic orbit ; horseshoe ; Shil'nikov phenomena ; 34 C 25-28 ; 58 F 05 ; 58 F 14 ; 58 F 30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a class of reversible, two-degree of freedom Hamiltonian systems possessing homoclinic orbits to a saddle-center: an equilibrium having two non-zero real and two nonzero imaginary eigenvalues. Under mild nondegeneracy conditions, we construct a two-parameter unfolding and show that there is a countable infinity of “secondary” homoclinic bifurcations in any neighborhood of the original system. We also demonstrate the existence of families of periodic orbits and of shifts on two symbols (horseshoes). The lack of hyperbolicity and the presence of conserved quantities make the analysis somewhat delicate. We discuss specific examples for which the nondegeneracy conditions can be explicitly checked but indicate that this is not always possible. We illustrate our results with numerical work.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Cellular and molecular life sciences 44 (1988), S. 772-774 
    ISSN: 1420-9071
    Keywords: Implantation ; blastocyst ; decidual reaction ; lipoxygenase ; prostaglandins ; leukotrienes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine
    Notes: Summary The present work investigates the possibility that lipoxygenase products are involved in the biochemical mechanisms of blastocyst implantation by utilizing nordihydroguaiaretic acid (NDGA) and caffeic acid (CA), inhibitors of lipoxygenase enzymes, and quinacrine (QU), an inhibitor of phospholipase-A2. It has been shown previously that inhibition of cyclooxygenase results in blockade of implantation. The inhibitors were dissolved in a standard medium and 5 μl of the solutions were micro-injected into the uterine horns of day-4 pregnant mice. The contralateral horns acted as controls and received only vehicle. A sham-operated group provided normal controls. In 14 NDGA-treated mice, the control horns contained 40 implantations while the treated horns contained only 6 small implantations and 8 resorbing sites. These control horns were comparable to the sham controls. In 14 CA-treated mice, treated horns contained 17 small implantations plus 4 resorptions, whereas the control horns contained 26 small implantations and 4 resorptions. Twelve QU-treated mice exhibited 7 small implantations and 4 resorptions in the treated horns, plus 24 small sites and no resorptions in the control horns. Fourteen sham-operated mice had 95 implantation sites and no resorptions in their 28 horns. The results provide evidence for the involvement of the lipoxygenase enzymes and phospholipase-A2 in the initial implantation process and in the subsequent development of early pregnancy.
    Type of Medium: Electronic Resource
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