Is there a Java equivalent or methodology for the typedef keyword in C++?

Question

Java has primitive types, objects and arrays and that's it. No typedefs.

If this is what you mean, you can simply extend the class you would like to typedef, e.g.:

public class MyMap extends HashMap<String, String> {}

There is no typedef in java as of 1.6, what you can do is make a wrapper class for what you want since you can't subclass final classes (Integer, Double, etc)

As others have mentioned before,
There is no typedef mechanism in Java.
I also do not support "fake classes" in general, but there should not be a general strict rule of thumb here:
If your code for example uses over and over and over a "generic based type" for example:

Map<String, List<Integer>> 

You should definitely consider having a subclass for that purpose.
Another approach one can consider, is for example to have in your code a deceleration like:

//@Alias Map<String, List<Integer>>  NameToNumbers;

And then use in your code NameToNumbers and have a pre compiler task (ANT/Gradle/Maven) to process and generate relevant java code.
I know that to some of the readers of this answer this might sound strange, but this is how many frameworks implemented "annotations" prior to JDK 5, this is what project lombok is doing and other frameworks.