For rare events, path probabilities often concentrate close to a predictable path, called instanton. First developed in statistical physics and field theory, instantons are action minimizers in a path integral representation. For chaotic deterministic systems, where no such action is known, shall we expect path probabilities to concentrate close to an instanton? We address this question for the dynamics of the terrestrial bodies of the Solar System. It is known that the destabilization of the inner Solar System might occur with a low probability, within a few hundred million years, or billion years, through a resonance between the motions of Mercury and Jupiter perihelia. In a simple deterministic model of Mercury dynamics, we show that the first exit time of such a resonance can be computed. We predict the related instanton and demonstrate that path probabilities actually concentrate close to this instanton, for events which occur within a few hundred million years. We discuss the possible implications for the actual Solar System.

中文翻译：

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破坏内部太阳系的瞬间。

对于罕见事件，路径概率通常集中在可预测的路径（称为瞬时）附近。瞬子首先在统计物理学和场论中发展，它们是路径积分表示中的动作最小化器。对于尚无此类动作的混沌确定性系统，我们是否可以期望路径概率集中在一个实例上？我们针对太阳系地面物体的动力学解决这个问题。众所周知，通过水星和木星近日点运动之间的共振，在几亿年或十亿年之内，内部太阳系的失稳可能性很小。在一个简单的水星动力学确定性模型中，我们表明可以计算出这种共振的第一个出口时间。我们预测相关的实例，并证明对于几亿年内发生的事件，路径概率实际上集中在此实例附近。我们讨论了对实际太阳系的可能影响。