时间可逆遍历映射和2015年Ian Snook奖
Time-Reversible Ergodic Maps and the 2015 Ian Snook Prize
摘要：
哈密顿力学的时间可逆性特征早已被推广到非哈密顿动力学系统，用基于反馈的恒温器和遍历器模拟非平衡稳态。典型的解是具有反转动量和不变坐标的多重分形吸引-排斥相空间对$(q,p)\longleftrightarrow (q,-p)$。弱控制的温度，$\propto p^2$和它的波动，导致遍历性，最近已经实现了在三维时间可逆模型的热传导谐振子。这种非平衡流的二维截面可以用时间可逆的耗散映射产生美学上有趣的吸引-排斥对。我们向读者挑战，寻找和探索这种时间可逆耗散映射。这个问题就是2015年的Snook Prize Problem。
英文摘要：
The time reversibility characteristic of Hamiltonian mechanics has long been extended to nonHamiltonian dynamical systems modeling nonequilibrium steady states with feedback-based thermostats and ergostats. Typical solutions are multifractal attractor-repellor phase-space pairs with reversed momenta and unchanged coordinates, $(q,p)\longleftrightarrow (q,-p)$ . Weak control of the temperature, $\propto p^2$ and its fluctuation, resulting in ergodicity, has recently been achieved in a three-dimensional time-reversible model of a heat-conducting harmonic oscillator. Two-dimensional cross sections of such nonequilibrium flows can be generated with time-reversible dissipative maps yielding æsthetically interesting attractor-repellor pairs. We challenge the reader to find and explore such time-reversible dissipative maps. This challenge is the 2015 Snook-Prize Problem.
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