fixate

Verb
  1. Attach (oneself) to a person or thing in a neurotic way (synset 202544031)
    "He fixates on his mother, even at the age of 40"
  2. Pay attention to exclusively and obsessively (synset 202175305)
    "The media are fixating on Princess Diana's death"
  3. Make fixed, stable or stationary (synset 200487934)
    "let's fix the picture to the frame"
  4. Become fixed (on) (synset 200487639)
    "Her eyes fixated on a point on the horizon"

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