Fear of flying persistent fear or anxiety when they consider flying, as well as during flying. They will avoid flying if they can, and the fear, anxiety, and avoidance cause significant distress and impair their ability to function. Take-off, bad weather, and turbulence appear to be the most anxiety provoking aspects of flying. The most extreme manifestations can include panic attacks or vomiting at the mere sight or mention of an aircraft or air travel. Around 60% of people with fear of flying report having some other anxiety disorder. The causes of flight phobia and the mechanisms by which it is maintained were
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