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The globally positive diffeomorphisms of the 2 n-dimensional annulus are important because they represent what happens close to a completely elliptic periodic point of a symplectic diffeomorphism where the torsion is positive definite. For these globally positive diffeomorphisms, an Aubry-Mather theory was developed by Garibaldi and Thieullen that provides the existence of some minimizing measures. Using the two Green bundles $${G_-}$$ and $${G_+}$$ that can be defined along the support of these minimizing measures, we will prove that there is a deep link between: [ABSTRACT FROM AUTHOR]

We prove that all the Tonelli Hamiltonians defined on the cotangent bundle $$T^*\mathbb {T}^n$$ of the $$n$$ -dimensional torus that have no conjugate points are $$C^0$$ integrable, i.e. $$T^*\mathbb {T}^n$$ is $$C^0$$ foliated by a family $$\mathcal {F}$$ of invariant $$C^0$$ Lagrangian graphs. Assuming that the Hamiltonian is $$C^\infty $$ , we prove that there exists a $$G_\delta $$ subset $$\mathcal {G}$$ of $$\mathcal {F}$$ such that the dynamics restricted to every element of $$\mathcal {G}$$ is strictly ergodic. Moreover, we prove that the Lyapunov exponents of every $$C^0$$ integrable Tonelli Hamiltonian are zero and deduce that the metric and topological entropies vanish. [ABSTRACT FROM AUTHOR]

We consider locally minimizing measures for conservative twist maps of the $d$-dimensional annulus and for Tonelli Hamiltonian flows defined on a cotangent bundle $T^*M$. For weakly hyperbolic measures of such type (i.e. measures with no zero Lyapunov exponents), we prove that the mean distance/angle between the stable and unstable Oseledets bundles gives an upper bound on the sum of the positive Lyapunov exponents and a lower bound on the smallest positive Lyapunov exponent. We also prove some more precise results. [ABSTRACT FROM PUBLISHER]

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Two species of the parasitic genus Striga, S. hermonthica (Del.) Benth. and S. gesnerioides Willd., cause severe damage to graminaceous and leguminous crops, respectively, in tropical and semi-tropical areas. Striga seed germination requires the presence of germination stimulants exuded by the roots of host plants. After attachment to the host root, the young parasite exhibits a subterranean stage of development during which it already induces considerable damage in the crop. Then, the parasite emerges from the soil, develops chlorophyllous shoots and, after flowering, produces a large number of minute seeds. Many field experiments performed in the USA to control another species (S. asiatica) have shown that application of chlorthal-dimethyl, dicamba or dinitroanilines prevented Striga emergence. Nevertheless the phenological stages of the parasite which are sensitive to the herbicides, as well as the mode of action of these products, are still unknown. Our experiments, performed in vitro, clearly show that chlorthal-dimethyl, dicamba or pendimethalin inhibit germination of S. hermonthica and S. gesnerioides seeds in the presence of natural germination stimulants. Moreover dicamba, clopyralid and linuron are able to induce the germination of S. gesnerioides seeds in the absence of stimulants (suicidal germination). Even if the mode of action of these herbicides in inhibition or induction of Striga seed germination has yet to be studied, such products can be useful to control Striga before attachment, thus preventing the crop from suffering the early damaging effect of the parasite. Moreover bromoxynil, ioxynil, bentazone and pyridate are potent inhibitors of photosynthesis in S. hermonthica, while they do not affect the hosts (maize and sorghum). Linuron also inhibits photosynthesis in the parasite, but it may affect these crops according to the rate applied. All these inhibitors of photosystem II could be used to control S. hermonthica after emergence, thus preventing seed production. [ABSTRACT FROM AUTHOR]