Invariant generators for generalized distributions

The existence of invariant generators for distributions satisfying a compatibility condition with the symmetry algebra is proved

Singular reduction of Dirac structures

The regular reduction of a Dirac manifold acted upon freely and properly by a Lie group is generalized to a nonfree action. For this, several facts about $G$-invariant vector fields and one-forms are shown

Poisson Reduction by Distributions

It is shown that the singular Poisson reduction procedure can be improved for a large class of situations. In addition, Poisson reduction of orbit type manifolds is carried out in detai

Poisson Reduction by Distributions

It is shown that the singular Poisson reduction procedure can be improved for a large class of situations. In addition, Poisson reduction of orbit type manifolds is carried out in detail

Shared Principles of Restoration Practice in the Chicago Wilderness Region

We describe the rules, norms, and strategies (institutional statements) that characterize ecological restoration across 10 organizations in the Chicago Wilderness region. Our use of Ostrom’s IAD ADICO grammar tool is novel in both context (non-extractive resource management) and data type (qualitative interviews). Results suggest that, in contrast to a focus on rules in the literature, restoration is overwhelmingly guided by strategies (institutional statements void of tangible or emotional sanctions). Moreover, a small, but critical set of norms exist. From over 1,700 institutional statements extracted, we found a suite of rich principles that guide behavior in all of the organizations: (1) qualify, don’t quantify; (2) listen to the land; (3) practice follow-up; (4) do no harm; (5) respond to sanctions from the land; (6) balance diverse internal stakeholders; and (7) balance diverse external factors. These principles suggest that Chicago Wilderness restorationists have a strong shared understanding upon which collective action and adaptive management occurs