PartofPrefacetothesecondedition
Themainpartofthisbookwaswrittentwentyyearsago.Theideasandmethodsofsymplecticgeometry,developedinthisbook,havenowfoundmanyapplicationsinmathematicalphysicsandinotherdomainsofappliedmathematics,aswellasinpuremathematicsitself.Especially,thetheoryofshortwaveasymptoticexpansionshasreachedaverysophiscatedlevel,withmanyimportantapplicationstooptics,wavetheory,acoustics,spectroscopy,andevenchemistry;thisdevelopmentwasparalleltothedevelopmentofthetheoriesofLagrangeandLegendresingularities,thatis,ofsingularitiesofcausticsandofwavefronts,oftheirtopologyandtheirperestroikas(inRussianmetamorphoseswerealwayscalled"perestroikas,"asin"Morseperestroika"fortheEnglish"Morsesurgery";nowthatthewordperestroikahasbecomeinternational,wemaypreservetheRussiantermintranslationandarenotobligedtosubstitute"metamorphoses"for"perestroikas"whenspeakingofwavefronts,caustics,andsoon. |
