We study initial value problems having dynamics ruled by discontinuous ordinary differential equations with the property of possessing a unique solution. We identify a precise class of such systems that we call solvable intitial value problems and we prove that for this class of problems the unique solution can always be obtained analytically via transfinite recursion. We present several examples including a nontrivial one whose solution yields, at an integer time, a real encoding of the halting set for Turing machines; therefore showcasing that the behavior of solvable systems is related to ordinal Turing computations.

翻译：我们研究由具有唯一解性质的不连续常微分方程支配动态的初值问题。我们识别出此类系统的一个精确类别，并将其称为可解初值问题，同时证明对于该类别的问题，其唯一解始终能通过超限递归以解析方式获得。我们给出了若干实例，其中包括一个非平凡例子：在整数时间点上，该例的解产生图灵机停机集的实数编码；由此表明可解系统的行为与序数图灵计算存在关联。