Local rigidity of actions of higher rank abelian groups and KAM method.

Damjanović, Danijela; Katok, Anatole

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We present an example of a rank-one partially mixing ℤ²-action which possesses a non-rigid factor and for which the Weak Closure Theorem fails. This is in sharp contrast to one-dimensional actions, which cannot display this type of behavior.

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The paradoxical place of small towns in sustainable development policies. What is beyond the images of “places where the living is easy”?

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Sustainable development policies have become new objectives of local actions since the implementation of the notion in the 1990s. Small towns promote images of places where the living is easy and with sustainable amenities like “natural” living environment. But, beyond these perceptions, operational sustainable development policies are quite occasional. Taking a sample of French small towns in the Auvergne region as examples, it is interesting to analyse this paradox of an interesting...