Matches in SemOpenAlex for { <https://semopenalex.org/work/W4302603091> ?p ?o ?g. }
Showing items 1 to 53 of
53
with 100 items per page.
- W4302603091 abstract "Let f_1 and f_2 be affine maps of the N-th dimensional affine space over the complex numbers, i.e., f_i(x):=A_i x + y_i (where each A_i is an N-by-N matrix and y_i is a given vector), and let x_1 and x_2 be vectors such that x_i is not preperiodic under the action of f_i for i=1,2. If none of the eigenvalues of the matrices A_i is a root of unity, then we prove that the set of pairs (n_1,n_2) of non-negative integers such that f_1^{n_1}(x_1)=f_2^{n_2}(x_2) is a finite union of sets of the form (m_1k + ell_1, m_2k + ell_2) where m_1, m_2, ell_1, ell_2 are given non-negative integers, and k is varying among all non-negative integers. Using this result, we prove that for any two self-maps Phi_i(x) := Phi_{i,0}(x)+y_i on a semiabelian variety X defined over the complex numbers (where Phi_{i,0} is an endomorphism of X and y_i is a given point of X), if none of the eigenvalues of the induced linear action DPhi_{i,0} on the tangent space at the identity 0 of X is a root of unity (for i=1,2), then for any two non-preperiodic points x_1,x_2, the set of pairs (n_1,n_2) of non-negative integers such that Phi_1^{n_1}(x_1) = Phi_2^{n_2}(x_2) is a finite union of sets of the form (m_1k + ell_1, m_2k + ell_2) where m_1,m_2,ell_1,ell_2 are given non-negative integers, and k is varying among all non-negative integers. We give examples to show that the above condition on eigenvalues is necessary and introduce certain geometric properties that imply such a condition. Our method involves an analysis of certain systems of polynomial-exponential equations and the p-adic exponential map for semiabelian varieties." @default.
- W4302603091 created "2022-10-07" @default.
- W4302603091 creator A5027386669 @default.
- W4302603091 creator A5078658360 @default.
- W4302603091 date "2016-04-09" @default.
- W4302603091 modified "2023-09-26" @default.
- W4302603091 title "The orbit intersection problem for linear spaces and semiabelian varieties" @default.
- W4302603091 doi "https://doi.org/10.48550/arxiv.1604.02529" @default.
- W4302603091 hasPublicationYear "2016" @default.
- W4302603091 type Work @default.
- W4302603091 citedByCount "0" @default.
- W4302603091 crossrefType "posted-content" @default.
- W4302603091 hasAuthorship W4302603091A5027386669 @default.
- W4302603091 hasAuthorship W4302603091A5078658360 @default.
- W4302603091 hasBestOaLocation W43026030911 @default.
- W4302603091 hasConcept C114614502 @default.
- W4302603091 hasConcept C116858840 @default.
- W4302603091 hasConcept C121332964 @default.
- W4302603091 hasConcept C158693339 @default.
- W4302603091 hasConcept C199360897 @default.
- W4302603091 hasConcept C206343339 @default.
- W4302603091 hasConcept C33923547 @default.
- W4302603091 hasConcept C41008148 @default.
- W4302603091 hasConcept C62520636 @default.
- W4302603091 hasConcept C84114770 @default.
- W4302603091 hasConcept C97137487 @default.
- W4302603091 hasConceptScore W4302603091C114614502 @default.
- W4302603091 hasConceptScore W4302603091C116858840 @default.
- W4302603091 hasConceptScore W4302603091C121332964 @default.
- W4302603091 hasConceptScore W4302603091C158693339 @default.
- W4302603091 hasConceptScore W4302603091C199360897 @default.
- W4302603091 hasConceptScore W4302603091C206343339 @default.
- W4302603091 hasConceptScore W4302603091C33923547 @default.
- W4302603091 hasConceptScore W4302603091C41008148 @default.
- W4302603091 hasConceptScore W4302603091C62520636 @default.
- W4302603091 hasConceptScore W4302603091C84114770 @default.
- W4302603091 hasConceptScore W4302603091C97137487 @default.
- W4302603091 hasLocation W43026030911 @default.
- W4302603091 hasOpenAccess W4302603091 @default.
- W4302603091 hasPrimaryLocation W43026030911 @default.
- W4302603091 hasRelatedWork W1483265251 @default.
- W4302603091 hasRelatedWork W1841979199 @default.
- W4302603091 hasRelatedWork W1980420279 @default.
- W4302603091 hasRelatedWork W2005706839 @default.
- W4302603091 hasRelatedWork W2030010946 @default.
- W4302603091 hasRelatedWork W2061144777 @default.
- W4302603091 hasRelatedWork W2131632800 @default.
- W4302603091 hasRelatedWork W2782885966 @default.
- W4302603091 hasRelatedWork W2963243507 @default.
- W4302603091 hasRelatedWork W3214428378 @default.
- W4302603091 isParatext "false" @default.
- W4302603091 isRetracted "false" @default.
- W4302603091 workType "article" @default.