Although chaotic attractors for autonomous dynamical systems show sensitive dependence on initial conditions, they also typically support a physical or natural measure that characterizes the statistical behavior of almost all initial conditions near the attractor with respect to a background measure such as Lebesgue. In this paper, we identify conditions under which a nonautonomous system that limits as $t\to -\infty$ to an autonomous system with a physical measure is guaranteed to possess a “nonautonomous physical measure” that limits to the physical measure of the autonomous system.

中文翻译：

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渐进自治动力系统的物理测量

尽管自主动力系统的混沌吸引子表现出对初始条件的敏感依赖性，但它们通常也支持物理或自然测量，该测量表征吸引子附近几乎所有初始条件相对于背景测量（例如勒贝格）的统计行为。在本文中，我们确定了非自治系统限制为的条件$t\to -\mathrm{无穷大}$具有物理量度的自治系统保证拥有限制于自治系统的物理量度的“非自治物理量度”。