?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=Systems+with+inheritance%3A+dynamics+of+distributions+with+conservation+of+support%2C+natural+selection+and++finite-dimensional+asymptotics&rft.creator=Gorban%2C+A.N.&rft.subject=Dynamical+Systems&rft.description=If+we+find+a+representation+of+an+infinite-dimensional+dynamical+system+as+a+nonlinear+kinetic+system+with+%7B%5Cit+conservation+of+supports%7D+of+distributions%2C+then+(after+some+additional+technical+steps)+we+can+state+that+the+asymptotics+is+finite-dimensional.+This+conservation+of+support+has+a+%7B%5Cit+quasi-biological+interpretation%2C+inheritance%7D+(if+a+gene+was+not+presented+initially+in+a+isolated+population+without+mutations%2C+then+it+cannot+appear+at+later+time).+These+quasi-biological+models+can+describe+various+physical%2C+chemical%2C+and%2C+of+course%2C+biological%0Asystems.+The+finite-dimensional+asymptotic+demonstrates+effects+of+%7B%5Cit+%60%60natural%22+selection%7D.+The+estimations+of+asymptotic+dimension+are+presented.+The+support+of+an+individual+limit+distribution+is+almost+always+small.+But+the+union+of+such+supports+can+be+the+whole+space+even+for+one+solution.+Possible+are+such+situations%3A+a+solution+is+a+finite+set+of+narrow+peaks+getting+in+time+more+and+more+narrow%2C+moving+slower+and+slower.+It+is+possible+that+these+peaks+do+not+tend+to+fixed+positions%2C+rather+they+continue+moving%2C+and+the+path+covered+tends+to+infinity+at+%24t+%5Crightarrow+%5Cinfty%24.+The+%7B%5Cit+drift+equations%7D+for+peaks+motion+are+obtained.+Various+types+of+stability+are+studied.%0AIn+example%2C+models+of+cell+division+self-synchronization+are%0Astudied.+The+appropriate+construction+of+notion+of+typicalness+in+infinite-dimensional+spaces+is+discussed%2C+and+the+%60%60completely+thin%22+sets+are+introduced.%0A&rft.date=2004-06&rft.type=Preprint&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.identifier=http%3A%2F%2Fcogprints.org%2F3815%2F1%2FOtbor2.pdf&rft.identifier=++Gorban%2C+A.N.++(2004)+Systems+with+inheritance%3A+dynamics+of+distributions+with+conservation+of+support%2C+natural+selection+and+finite-dimensional+asymptotics.++%5BPreprint%5D+++++&rft.relation=http%3A%2F%2Fcogprints.org%2F3815%2F