How does Tomcat create threads internally?

I'm writing a Tomcat application which need to maintain some internal states across different requests, so I need share something between different threads created by Tomcat. My question is, if I write code like this, will Map (which is static to the class) be shared between threads created by Tomcat.

public class sessionManager extends HttpServlet {
    private static HashMap<Integer, String> Map;

    protected void doPost(HttpServletRequest request, HttpServletResponse response) throws ServletException, IOException {
        // logic
    }
}

I guess what I really don't get is how does Tomcat create many threads from a single class.