The way I see it, entrepreneurship is not really a science in itself, but more of a context for other sciences. So you could research the subject from many different point of views. Some examples are:
Psychology: What personal traits makes an entrepreneur successful? Why do some people become Serial Entrepreneurs?
Organization theory: How should a startup company be organized?
Economics: How does the economy/external factors affect small companies?
Finance: How should a small company manage its finances?