The charts can be configured to be updated at preset intervals with the new data. The idea is to periodically update chart.dataProvider (or chart.dataSet[x].dataProvider in case of Stock chart) with the new data points, then just call chart.validateData() for the chart to take in the new data. Here's a working example.
The data updates can be loaded using some AJAX techniques, like jQuery's getJSON method. And here's an example of real-time Stock chart.
The same technique can be used with amMap - just update dataProvider of the map and call map.validateData(); method.
Serial chart example
See the Pen Real-time serial chart by amCharts (@amcharts) on CodePen.light
Stock Chart example
See the Pen Stock Chart multiple data sets with real time data by amCharts (@amcharts) on CodePen.light