Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two

We consider the billiard dynamics in a non-compact set of ℝ d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called quenched random Lorentz tube. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.

Recurrence for quenched random Lorentz tubes

We consider the billiard dynamics in a striplike set that is tessellated by countably many translated copies of the same polygon. A random configuration of semidispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global choice of scatterers, is called quenched random Lorentz tube. We prove that under general conditions, almost every system in the ensemble is recurrent.

Enchanting resilience: relations of care and people-place connections in agriculture

The practices and decision-making of contemporary agricultural producers are governed by a multitude of different, and sometimes competing, social, economic, regulatory, environmental and ethical imperatives. Understanding how they negotiate and adapt to the demands of this complex and dynamic environment is crucial in maintaining an economically and environmentally viable and resilient agricultural sector. This paper takes a socio-cultural approach to explore the development of social resilience within agriculture through an original and empirically grounded discussion of people-place connections amongst UK farmers. It positions enchantment as central in shaping farmers' embodied and experiential connections with their farms through establishing hopeful, disruptive and demanding ethical practices. Farms emerge as complex moral economies in which an expanded conceptualisation of the social entangles human and non-human actants in dynamic and contextual webs of power and responsibility. While acknowledging that all farms are embedded within broader, nested levels, this paper argues that it is at the micro-scale that the personal, contingent and embodied relations that connect farmers to their farms are experienced and which, in turn, govern their capacity to develop social resilience.