{"title":"FINITE TIME BLOW-UP IN A MATHEMATICAL MODEL OF SUB-ATOMIC PARTICLE OSCILLATIONS","authors":"I. Ncube","doi":"10.17654/DS030030077","DOIUrl":"https://doi.org/10.17654/DS030030077","url":null,"abstract":"","PeriodicalId":330387,"journal":{"name":"Far East Journal of Dynamical Systems","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115846525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"METHOD OF MODAL SYNTHESIS IN THE DYNAMICS OF A DEFORMABLE SPATIAL STRUCTURE","authors":"Moussa Sylla, Saraka Jean Modeste Kouassi","doi":"10.17654/ds030030103","DOIUrl":"https://doi.org/10.17654/ds030030103","url":null,"abstract":"","PeriodicalId":330387,"journal":{"name":"Far East Journal of Dynamical Systems","volume":"320 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116632279","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"ENTROPY OF A SEMI-FLOW FOR RECURRENCE TIME","authors":"Wei Wang","doi":"10.17654/DS030020059","DOIUrl":"https://doi.org/10.17654/DS030020059","url":null,"abstract":"","PeriodicalId":330387,"journal":{"name":"Far East Journal of Dynamical Systems","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134506804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"ON ENTROPIES AND COMPLEXITY FOR AMENABLE ACTIONS GROUPS","authors":"A. Mesón, F. Vericat","doi":"10.17654/ds030020037","DOIUrl":"https://doi.org/10.17654/ds030020037","url":null,"abstract":"","PeriodicalId":330387,"journal":{"name":"Far East Journal of Dynamical Systems","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131705033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"PERMANENCE AND GLOBAL STABILITY ANALYSIS OF A DELAYED THREE SPECIES PREDATOR-PREY MODEL WITH COOPERATION AMONG PREYS","authors":"S. Kundu, S. Maitra","doi":"10.17654/ds030010011","DOIUrl":"https://doi.org/10.17654/ds030010011","url":null,"abstract":"","PeriodicalId":330387,"journal":{"name":"Far East Journal of Dynamical Systems","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124554215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"NEW EXACT SOLUTIONS AND KIND WAVE EXCITATIONS OF THE (2+1)-DIMENSIONAL DISSIPATIVE ZABOLOTSKAYA-KHOKHLOV EQUATION","authors":"Dan Zhuang, Songhua Ma","doi":"10.17654/ds030010027","DOIUrl":"https://doi.org/10.17654/ds030010027","url":null,"abstract":"","PeriodicalId":330387,"journal":{"name":"Far East Journal of Dynamical Systems","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134100540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"COMPLEX WAVE EXCITATIONS OF THE (2+1) -DIMENSIONAL BOITI-LEON-PEMPINELLI SYSTEM","authors":"Liping Gong, Songhua Ma","doi":"10.17654/ds030010001","DOIUrl":"https://doi.org/10.17654/ds030010001","url":null,"abstract":"","PeriodicalId":330387,"journal":{"name":"Far East Journal of Dynamical Systems","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123910339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"DEGREE, MIXING, AND ABSOLUTELY CONTINUOUS SPECTRUM OF COCYCLES WITH VALUES IN COMPACT LIE GROUPS","authors":"R. T. Aldecoa","doi":"10.17654/DS030040135","DOIUrl":"https://doi.org/10.17654/DS030040135","url":null,"abstract":"We consider skew products $$T_phi:Xtimes Gto Xtimes G,~~(x,g)mapsto(F_1(x),g;!phi(x)),$$ where $X$ is a compact manifold with probability measure, $G$ a compact Lie group with Lie algebra $frak g$, $F_1:Xto X$ the time-one map of a measure-preserving flow, and $phiin C^1(X,G)$ a cocycle. Then, we define the degree of $phi$ as a suitable function $P_phi M_phi:Xtofrak g$, we show that it transforms in a natural way under Lie group homomorphisms and under the relation of $C^1$-cohomology, and we explain how it generalises previous definitions of degree of a cocycle. For each finite-dimensional irreducible representation $pi$ of $G$, and $frak g_pi$ the Lie algebra of $pi(G)$, we define in an analogous way the degree of $picircphi$ as a suitable function $P_{picircphi}M_{picircphi}:Xtofrak g_pi$. If $F_1$ is uniquely ergodic and the functions $picircphi$ diagonal, or if $T_phi$ is uniquely ergodic, then the degree of $phi$ reduces to a constant in $frak g$ given by an integral over $X$. As a by-product, we obtain that there is no uniquely ergodic skew product $T_phi$ with nonzero degree if $G$ is a connected semisimple compact Lie group. \u0000Next, we show that $T_phi$ is mixing in the orthocomplement of the kernel of $P_{picircphi}M_{picircphi}$, and under some additional assumptions we show that $U_phi$ has purely absolutely continuous spectrum in that orthocomplement if $(iP_{picircphi}M_{picircphi})^2$ is strictly positive. Summing up these results for each $pi$, one obtains a global result for the mixing and the absolutely continuous spectrum of $T_phi$. As an application, we present four explicit cases: when $G$ is a torus, $G=SU(2)$, $G=SO(3,mathbb R)$, and $G=U(2)$. In each case, the results we obtain are new, or generalise previous results. \u0000Our proofs rely on new results on positive commutator methods for unitary operators.","PeriodicalId":330387,"journal":{"name":"Far East Journal of Dynamical Systems","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132143292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}