1. A method of monitoring an aircraft engine, comprising: electronically collecting time history measurements regarding variables related to a current engine and its environment, including a first set of measurements regarding endogenic variables describing behavior of the engine and a second set of measurements regarding exogenic variables describing acquisition context, during each acquisition; standardizing measurements related to the endogenic variables taking account of measurements related to the exogenic variables to form an entry point corresponding to a condition of the current engine in a multi-dimensional space, for each acquisition; projecting, using a determined compression technique, each entry point in the multi-dimensional space onto an image point on a previously constructed map, to form a sequence of image points on the map reflecting a distribution of entry points in the multi-dimensional space, the image points forming a current trajectory representative of a change to the conditions of the current engine; comparing a portion of an end of the current trajectory with previously recorded portions of trajectories of aircraft engines kept in a database to search for similar trajectories; analyzing statistical variation of the end of current trajectory as a function of the similar trajectories; and forecasting maintenance operations on the current engine.