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XIE, FG; HAO, BL
COUNTING THE NUMBER OF PERIODS IN ONE-DIMENSIONAL MAPS WITH MULTIPLE CRITICAL-POINTS
Source PublicationPHYSICA A
KeywordSymbolic Dynamics Cubic Map Endomorphisms Cycles
AbstractThe problem of counting the number of different periodic orbits in continuous maps of an interval is solved. A map with m monotone pieces (laps) and m - 1 critical points may have at most m - 1 independent kneading sequences, which provide the most convenient parameters for the map. When one or more kneading sequences are kept constant or bound to vary simultaneously, Various degenerated cases of the map arise. The number of period n orbits of the general m-lap map as well as various degenerated cases is given by combinations of N-k(n) with k equal to or less than m, where N-m(n) is the number of period n orbits of a particular kind of degenerated m-lap map with only one kneading sequence. The quantity N-m(n) may be calculated or enumerated by many different methods, which are all discussed in this paper. We also give tabulated values for N-m(n) for m = 2 to 7.
1994
ISSN0378-4371
Volume202Issue:40910Pages:237-263
Subject AreaPhysics
Indexed BySCI
Document Type期刊论文
Identifierhttp://ir.itp.ac.cn/handle/311006/11970
Collection理论物理所科研产出_SCI论文
Recommended Citation
GB/T 7714
XIE, FG,HAO, BL. COUNTING THE NUMBER OF PERIODS IN ONE-DIMENSIONAL MAPS WITH MULTIPLE CRITICAL-POINTS[J]. PHYSICA A,1994,202(40910):237-263.
APA XIE, FG,&HAO, BL.(1994).COUNTING THE NUMBER OF PERIODS IN ONE-DIMENSIONAL MAPS WITH MULTIPLE CRITICAL-POINTS.PHYSICA A,202(40910),237-263.
MLA XIE, FG,et al."COUNTING THE NUMBER OF PERIODS IN ONE-DIMENSIONAL MAPS WITH MULTIPLE CRITICAL-POINTS".PHYSICA A 202.40910(1994):237-263.
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