Abstract
This work is devoted to the study of some one-dimensional dynamical systems with discrete time, for which rounding to the different number of decimal places leads to the qualitative change in orbits. It is proved that the behavior of the trajectories of dynamical systems essentially depends on the order of rounding.
Highlights
@IFIA äå f " äåÿêå âiäîáðàæåííÿ âiäðiçêà I = [0, 1] ó ñåáå àáî êîëà S1D ÿêå áóäåìî îòîòîæíþâàòè ç âiäðiçêîì I çi ñêëå1íèìè êiíöÿìèF
Çà óìîâ ÷èñëîâîãî îá÷èñëåííÿ òðà1êòîðiñèñòåìè @IFIAD ÿê ïðàâèëîD çàñòîE ñîâóþòü îêðóãëåííÿ äî äåÿêîôiêñîâàíîêiëüêîñòi äåñÿòêîâèõ çíàêiâ ïiñëÿ êîìèF Öå îçíà÷à1D ùî ñèñòåìà @IFIA çàìiíþ1òüñÿ íà äèíàìi÷íó ñèñòåìó âèãëÿE äó xi+1
Ïîðiâíþ1ìî ðåçóëüòàòè äiäèíàìi÷íîñèñòåìè çàëåæíî âiä òîãîD äî ÿêîãî çíàêà çäiéñíþâàëè îêðóãëåííÿF Äëÿ öüîãî ïiäðàõîâó1ìî êiëüêiñòü òî÷îê íà êîæíîìó ç ïðîìiæêiâF Öÿ êiëüêiñòü ìà1 çàëèøàòèñÿ ïîñòiéíîþ íà âiäïîâiäíèõ ïðîìiæêàõ çà óìîâ ðiçíèõ ïîðÿäêiâ îêðóãëåííÿF Ðåçóëüòàòè äëÿ ðîçãëÿíóòèõ ôóíêöié fi, i = 1, 2 íàâåäåíî â òàáëF IDPF
Summary
Äîñëiäæåíî ïîâåäiíêó äåÿêèõ îäíîâèìiðíèõ äèíàìi÷íèõ ñèñòåì iç äèñêðåòíèì ÷àñîì, äëÿ ÿêèõ îá÷èñëåííÿ ç îêðóãëåííÿì äî ðiçíîêiëüêîñòi ðîçðÿäiâ ïiñëÿ êîìè çóìîâëþ1 ÿêiñíó çìiíó îðáiò, òîáòî ïîÿâó íîâèõ äèíàìi÷íèõ ñèñòåì. Äëÿ ÿêîîáëàñòü âèçíà÷åííÿ ôóíêöif 1 ïiäìíîæèíîþ òî÷îê ç I àáî S1D ó äåñÿòêîâîìó çîáðàæåíi ÿêèõ @áåç äåâ9ÿòêè ó ïåðiîäiA óñi öèôðè ïiñëÿ êîìèD ïî÷èíàþ÷è ç öèôðè ïiä íîìåðîì k + 1D 1 íóëiF Âiäîáðàæåííÿ fñèñòåìè @IFQA " öå ñóïåðïîçèöiÿ âiäîáðàæåííÿ f òà âiäîáðàæåííÿ îêðóãëåííÿ äî k çíàêiâ ïiñëÿ êîìèF Ó öüîìó ðîçäiëi íàâåäåìî ïðèêëàäè îäíîâèìiðíèõ äèíàìi÷íèõ ñèñòåì iç íåðåãóëÿðíîþ ïîâåäiíêîþ çà óìîâè çìiíè ïîðÿäêó îêðóãëåííÿF
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