fixate

(verb) attach (oneself) to a person or thing in a neurotic way. Examples: "He fixates on his mother, even at the age of 40."

(verb) pay attention to exclusively and obsessively. Examples: "The media are fixating on princess diana's death."

(verb) make fixed, stable or stationary. Synonyms: fix. Examples: "Let's fix the picture to the frame."

(verb) become fixed (on). Synonyms: settle on. Examples: "Her eyes fixated on a point on the horizon."