Pub Date : 2023-06-01DOI: 10.1134/S2070046623020061
M. C. Siegel
{"title":"Infinite Series Whose Topology of Convergence Varies From Point to Point","authors":"M. C. Siegel","doi":"10.1134/S2070046623020061","DOIUrl":"https://doi.org/10.1134/S2070046623020061","url":null,"abstract":"","PeriodicalId":44654,"journal":{"name":"P-Adic Numbers Ultrametric Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73386627","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}
Pub Date : 2023-03-01DOI: 10.1134/s207004662301003x
I. A. Sattarov, E. T. Aliev
We consider $$(1,2)$$ -rational functions given on the field of $$p$$ -adic numbers $${mathbb Q}_p$$ . In general, such a function has four parameters. We study the case when such a function has two fixed points and show that when there are two fixed points then $$(1,2)$$ -rational function is conjugate to a two-parametric $$(1,2)$$ -rational function. Depending on these two parameters we determine type of the fixed points, find Siegel disks and the basin of attraction of the fixed points. Moreover, we classify invariant sets and study ergodicity properties of the function on each invariant set. We describe 2- and 3-periodic orbits of the $$p$$ -adic dynamical systems generated by the two-parametric $$(1,2)$$ -rational functions.
{"title":"Ergodicity and Periodic Orbits of $$p$$-Adic $$(1,2)$$-Rational Dynamical Systems with Two Fixed Points","authors":"I. A. Sattarov, E. T. Aliev","doi":"10.1134/s207004662301003x","DOIUrl":"https://doi.org/10.1134/s207004662301003x","url":null,"abstract":"We consider $$(1,2)$$ -rational functions given on the field of $$p$$ -adic numbers $${mathbb Q}_p$$ . In general, such a function has four parameters. We study the case when such a function has two fixed points and show that when there are two fixed points then $$(1,2)$$ -rational function is conjugate to a two-parametric $$(1,2)$$ -rational function. Depending on these two parameters we determine type of the fixed points, find Siegel disks and the basin of attraction of the fixed points. Moreover, we classify invariant sets and study ergodicity properties of the function on each invariant set. We describe 2- and 3-periodic orbits of the $$p$$ -adic dynamical systems generated by the two-parametric $$(1,2)$$ -rational functions.","PeriodicalId":44654,"journal":{"name":"P-Adic Numbers Ultrametric Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134996118","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}
Pub Date : 2023-03-01DOI: 10.1134/s2070046623010016
M. Restrepo Borrero, Vatsala Srivastava, K. Shamseddine
{"title":"On a New Measure on the Levi-Civita Field $$ mathcal{R} $$","authors":"M. Restrepo Borrero, Vatsala Srivastava, K. Shamseddine","doi":"10.1134/s2070046623010016","DOIUrl":"https://doi.org/10.1134/s2070046623010016","url":null,"abstract":"","PeriodicalId":44654,"journal":{"name":"P-Adic Numbers Ultrametric Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84873392","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}
Pub Date : 2023-03-01DOI: 10.1134/S2070046623010053
A. Escassut
{"title":"Number of Zeros of Exponential Polynomials in Zero Residue Characteristic","authors":"A. Escassut","doi":"10.1134/S2070046623010053","DOIUrl":"https://doi.org/10.1134/S2070046623010053","url":null,"abstract":"","PeriodicalId":44654,"journal":{"name":"P-Adic Numbers Ultrametric Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73800546","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}
Pub Date : 2022-12-01DOI: 10.1134/s2070046622050065
K. Khachatryan, H. S. Petrosyan
{"title":"On the Constructive Solvability of a Two-Dimensional Nonlinear Integral Equation Arising in the Theory of $$p$$-Adic Strings","authors":"K. Khachatryan, H. S. Petrosyan","doi":"10.1134/s2070046622050065","DOIUrl":"https://doi.org/10.1134/s2070046622050065","url":null,"abstract":"","PeriodicalId":44654,"journal":{"name":"P-Adic Numbers Ultrametric Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85907648","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}
Pub Date : 2022-12-01DOI: 10.1134/s2070046622040057
S. Volosivets, A. N. Mingachev
{"title":"On the Magnitude of Fourier Coefficients with Respect to the Character System of $$mathbb Z_p$$","authors":"S. Volosivets, A. N. Mingachev","doi":"10.1134/s2070046622040057","DOIUrl":"https://doi.org/10.1134/s2070046622040057","url":null,"abstract":"","PeriodicalId":44654,"journal":{"name":"P-Adic Numbers Ultrametric Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83814460","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}
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