Emetophobia in which the phobic person will go to great lengths to avoid even potential situations that could even be perceived as "threatening". Emetophobia is clinically considered an "elusive predicament" because limited research has been done pertaining to it. The fear of vomiting receives little attention compared with other irrational fears. Frank M. Dattilio. "Emetic Exposure and Desensitization Procedures in the Reduction of Nausea and a Fear of Emesis." "Clinical Case Studies" 2.3 (2003): 199-210.</ref> The event of vomiting may make anyone with this peculiar phobia flee the scene. Some may fear someone throwing up, while others may fear themselves throwing
Irrational rotation between the additive and multiplicative notations is the group isomorphism It can be shown that is an isometry. There is a strong distinction in circle rotations that depends on whether is rational or irrational. Rational rotations are less interesting examples of dynamical systems because if formula_4 and formula_5, then formula_6 when formula_7. It can also be shown that formula_8 when formula_9. Irrational rotations form a fundamental example in the theory of dynamical systems. According to the Denjoy theorem, every orientation-preserving -diffeomorphism of the circle with an irrational rotation number is topologically conjugate to . An irrational rotation is a measure-preserving