Get fields of Delegate class reflection

I have class

public class Car {

    private String name;
    private int year;

    public Car(String name, int year) {
        this.name = name;
        this.year = year;
    }

    public String getName() {
        return name;
    }

    public void setName(String name) {
        this.name = name;
    }

    public int getYear() {
        return year;
    }

    public void setYear(int year) {
        this.year = year;
    }
}

Person Class

public class Person {

    private String name;
    private int age;
    private boolean adult;

    private Car car;

    public Person(String name, int age, final Car car) {
        this.name = name;
        this.age = age;
        this.car = car;
    }

    public Person(String name, int age) {
        this.name = name;
        this.age = age;
    }

    public Car getCar() {
        return car;
    }

    public void setCar(Car car) {
        this.car = car;
    }

    public String getName() {
        return name;
    }

    public int getAge() {
        return age;
    }

    public boolean isAdult() {
        return adult;
    }

    public void setAdult(boolean adult) {
        this.adult = adult;
    }

    @Override
    public String toString() {
        return "Person{" +
                "name='" + name + '\'' +
                ", age=" + age +
                ", adult=" + adult +
                '}';
    }
}

I have to get fields using reflection and set / get values dynamically.

I am keeping them in a map

Map<String, Field> map = new HashMap<>();

        for (Field field : Person.class.getDeclaredFields()) {
            field.setAccessible(true);
            map.put(field.getName(), field);
        }

        System.out.println(map);

I have the map now with all the fields later on I can get/set any attribute

What I cannot get it how do I store Car in the map like

"car.name" , <FIELD> 
"car.age" , <FIELD>

later on I can get from map like mapp.get("car.name", person) that would return the car name