The words of possession come with these feelings--"my hiking trail, my pond, my song", but it's not an ownership thing at all. It's a sense of admission--I've given a ticket to this particular unwieldy tourist to make a temporary home in my dreamscape. I sense that I am at home, and so these things must belong to me. Maybe that's a marvel in the world of notions--there are no deeds, and the property ownership is entirely a figment of the imagination.
Of course, a tear erupts from my eye for just a moment, like the commercial, that all ownership is a figment, but that's just a passing cinematic denial, and not a desire to reorder the nature of property.
I notice that I "have" a fishing lake, a favorite trail, and even a cinnamon roll source. Last year, I remember writing how I "owned" herons. Perhaps it is a problem of attachment. But I listen to my favorite guitar solo, and it is "mine", too, though the rights all belong to a Yorkshire guitarist and his assignees, thousands of miles away.