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Map variable help

List<String> mergeFields = new List<String>{'Contact.AccountId','Contact.Name','Application__c.Name','Application__c.Contact__c'};
List<string> objectNames = new List<string>{'Contact','Application__c'};

I have a two list of strings. I want to use a Map variable to assign key value pairs. for objectNames key is Contact, values should contain Contact.AccountId','Contact.Name and for objectNames key is Application__c, values should contain Application__c.Name','Application__c.Contact__c
In reality , the mergefields and objectnames could be anything related to eachother not only Contact and Application__c

Map <string,List<String>> objectMap = new Map <string,List<String>>();

Please help on assigning a key value pair
If you know that they will always have a period in them, you could do the following
List<String> mergeFields = new List<String> {

Map<String, List<String>> objectMap = new Map<String, List<String>>();
for (String field : mergeFields) {
    String objName = field.split('.').get(0);

    if (!objectMap.containsKey(objName)) {
        objectMap.put(objName, new List<String>());


NOTE: This code has not been tested and may contain typographical or logical errors
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