Mathematical Sciences: RUI: Nonsingular Ergodic Theory

席尔瓦教授将研究遍历理论中的非奇异连接。非奇异连接是由D. Rudolph提出并由Silva和Rudolph先前研究过的一个概念，它将在Silva对非奇异无限保测度变换的研究中发挥关键作用。这个项目涉及遍历理论的研究。遍历理论一般关注理解系统的平均行为，其动力学过于复杂或混乱，无法在微观细节上进行跟踪。通常遍历理论包含一个保持自然概率测度的动力学。席尔瓦教授的研究关注的是这种良好性质无法维持的系统。

Professor Silva will study nonsingular joinings in ergodic theory. Nonsingular joinings, a concept introduced by D. Rudolph and studied previously by Silva and Rudolph, will play a pivotal role in Silva's study of nonsingular infinite measure- preserving transformations. This project involves research in ergodic theory. Ergodic theory in general concerns understanding the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. Usually ergodic theory involves a dynamics which preserves a natural probability measure. Professor Silva's research concerns systems where this nice property fails to hold.