Matches in SemOpenAlex for { <https://semopenalex.org/work/W2962782908> ?p ?o ?g. }
Showing items 1 to 85 of
85
with 100 items per page.
- W2962782908 endingPage "4893" @default.
- W2962782908 startingPage "4871" @default.
- W2962782908 abstract "Let $x$ and $y$ be points in a billiard table $M=M(sigma)$ in$mathbb{mathbb{R}}^{2}$ that is bounded by a curve $sigma$. Weassume $sigmainSigma_{r}$ with $rgeq2$, where $Sigma_{r}$is the set of simple closed $C^{r}$ curves in $mathbb{R}^{2}$ withpositive curvature. A subset $B$ of $Msetminus{x,y}$ is calleda blocking set for the pair $(x,y)$ if every billiard pathin $M$ from $x$ to $y$ passes through a point in $B$. If a finiteblocking set exists, the pair $(x,y)$ is called secure in$M;$ if not, it is called insecure. We show that for $sigma$in a dense $G_{delta}$ subset of $Sigma_{r}$ with the $C^{r}$topology, there exists a dense $G_{delta}$ subset $mathcal{mathcal{R}=R}(sigma)$of $M(sigma)times M(sigma)$ such that $(x,y)$ is insecure in$M(sigma)$ for each $(x,y)inmathcal{R}$. In this sense, for thegeneric Birkhoff billiard, the generic pair of interior points isinsecure. This is related to a theorem of S. Tabachnikov [24]that $(x,y)$ is insecure for all sufficiently close points$x$ and $y$ on a strictly convex arc on the boundary of a smoothtable." @default.
- W2962782908 created "2019-07-30" @default.
- W2962782908 creator A5053411993 @default.
- W2962782908 creator A5054670548 @default.
- W2962782908 date "2016-05-01" @default.
- W2962782908 modified "2023-10-14" @default.
- W2962782908 title "Generic absence of finite blocking for interior points of Birkhoff billiards" @default.
- W2962782908 cites W1506380541 @default.
- W2962782908 cites W1968499554 @default.
- W2962782908 cites W1969810742 @default.
- W2962782908 cites W1984614267 @default.
- W2962782908 cites W2014963906 @default.
- W2962782908 cites W2031169713 @default.
- W2962782908 cites W2033460686 @default.
- W2962782908 cites W2047029313 @default.
- W2962782908 cites W2070178103 @default.
- W2962782908 cites W2079694968 @default.
- W2962782908 cites W2085772715 @default.
- W2962782908 cites W2088834857 @default.
- W2962782908 cites W2136733034 @default.
- W2962782908 cites W2160296092 @default.
- W2962782908 cites W2324853665 @default.
- W2962782908 cites W2950646207 @default.
- W2962782908 cites W2962850301 @default.
- W2962782908 cites W2963822979 @default.
- W2962782908 cites W3102186910 @default.
- W2962782908 cites W3104268702 @default.
- W2962782908 cites W4212958445 @default.
- W2962782908 cites W4255340725 @default.
- W2962782908 doi "https://doi.org/10.3934/dcds.2016010" @default.
- W2962782908 hasPublicationYear "2016" @default.
- W2962782908 type Work @default.
- W2962782908 sameAs 2962782908 @default.
- W2962782908 citedByCount "1" @default.
- W2962782908 countsByYear W29627829082018 @default.
- W2962782908 crossrefType "journal-article" @default.
- W2962782908 hasAuthorship W2962782908A5053411993 @default.
- W2962782908 hasAuthorship W2962782908A5054670548 @default.
- W2962782908 hasBestOaLocation W29627829081 @default.
- W2962782908 hasConcept C112680207 @default.
- W2962782908 hasConcept C114614502 @default.
- W2962782908 hasConcept C121332964 @default.
- W2962782908 hasConcept C134306372 @default.
- W2962782908 hasConcept C193605512 @default.
- W2962782908 hasConcept C195065555 @default.
- W2962782908 hasConcept C2524010 @default.
- W2962782908 hasConcept C2778049214 @default.
- W2962782908 hasConcept C33923547 @default.
- W2962782908 hasConcept C34388435 @default.
- W2962782908 hasConcept C62354387 @default.
- W2962782908 hasConcept C62520636 @default.
- W2962782908 hasConceptScore W2962782908C112680207 @default.
- W2962782908 hasConceptScore W2962782908C114614502 @default.
- W2962782908 hasConceptScore W2962782908C121332964 @default.
- W2962782908 hasConceptScore W2962782908C134306372 @default.
- W2962782908 hasConceptScore W2962782908C193605512 @default.
- W2962782908 hasConceptScore W2962782908C195065555 @default.
- W2962782908 hasConceptScore W2962782908C2524010 @default.
- W2962782908 hasConceptScore W2962782908C2778049214 @default.
- W2962782908 hasConceptScore W2962782908C33923547 @default.
- W2962782908 hasConceptScore W2962782908C34388435 @default.
- W2962782908 hasConceptScore W2962782908C62354387 @default.
- W2962782908 hasConceptScore W2962782908C62520636 @default.
- W2962782908 hasIssue "9" @default.
- W2962782908 hasLocation W29627829081 @default.
- W2962782908 hasLocation W29627829082 @default.
- W2962782908 hasOpenAccess W2962782908 @default.
- W2962782908 hasPrimaryLocation W29627829081 @default.
- W2962782908 hasRelatedWork W1998107763 @default.
- W2962782908 hasRelatedWork W2026219749 @default.
- W2962782908 hasRelatedWork W2047507885 @default.
- W2962782908 hasRelatedWork W2080996569 @default.
- W2962782908 hasRelatedWork W2950242289 @default.
- W2962782908 hasRelatedWork W2951601310 @default.
- W2962782908 hasRelatedWork W2963756985 @default.
- W2962782908 hasRelatedWork W4210415442 @default.
- W2962782908 hasRelatedWork W4297631805 @default.
- W2962782908 hasRelatedWork W2006342768 @default.
- W2962782908 hasVolume "36" @default.
- W2962782908 isParatext "false" @default.
- W2962782908 isRetracted "false" @default.
- W2962782908 magId "2962782908" @default.
- W2962782908 workType "article" @default.