Matches in SemOpenAlex for { <https://semopenalex.org/work/W4313303885> ?p ?o ?g. }
Showing items 1 to 65 of
65
with 100 items per page.
- W4313303885 abstract "We study the breakdown of rotational invariant tori in 2D and 4D standard maps by implementing three different methods. First, we analyze the domains of analyticity of a torus with given frequency through the computation of the Lindstedt series expansions of the embedding of the torus and the drift term. The Pad'e approximants provide the shape of the analyticity domains by plotting the poles of the polynomial at the denominator of the approximants. Secondly, we implement a Newton method to construct the embedding of the torus; the breakdown threshold is then estimated by looking at the blow-up of the Sobolev norms of the embedding. Finally, we implement an extension of Greene method to get information on the breakdown threshold of an invariant torus with irrational frequency by looking at the stability of the periodic orbits with periods approximating the frequency of the torus. We apply these methods to 2D and 4D standard maps. The 2D maps can either be conservative (symplectic) or dissipative ( more precisely, conformally symplectic, namely a dissipative map with the geometric property to transform the symplectic form into a multiple of itself). The 4D maps are obtained coupling $(i)$ two symplectic standard maps, or $(ii)$ two conformally symplectic standard maps, or $(iii)$ a symplectic and a conformally symplectic standard map. Concerning the results, Pad'e and Newton methods perform well and provide reliable and consistent results (although we implemented Newton method only for symplectic and conformally symplectic maps). Our implementation of the extension of Greene method is inconclusive, since it is computationally expensive and delicate, especially in 4D non-symplectic maps, also due to the existence of Arnold tongues." @default.
- W4313303885 created "2023-01-06" @default.
- W4313303885 creator A5024028420 @default.
- W4313303885 creator A5040844225 @default.
- W4313303885 creator A5089916909 @default.
- W4313303885 date "2022-12-28" @default.
- W4313303885 modified "2023-09-25" @default.
- W4313303885 title "Breakdown of rotational tori in 2D and 4D conservative and dissipative standard maps" @default.
- W4313303885 doi "https://doi.org/10.48550/arxiv.2212.13960" @default.
- W4313303885 hasPublicationYear "2022" @default.
- W4313303885 type Work @default.
- W4313303885 citedByCount "0" @default.
- W4313303885 crossrefType "posted-content" @default.
- W4313303885 hasAuthorship W4313303885A5024028420 @default.
- W4313303885 hasAuthorship W4313303885A5040844225 @default.
- W4313303885 hasAuthorship W4313303885A5089916909 @default.
- W4313303885 hasBestOaLocation W43133038851 @default.
- W4313303885 hasConcept C121332964 @default.
- W4313303885 hasConcept C134306372 @default.
- W4313303885 hasConcept C154945302 @default.
- W4313303885 hasConcept C168619227 @default.
- W4313303885 hasConcept C190470478 @default.
- W4313303885 hasConcept C202444582 @default.
- W4313303885 hasConcept C2524010 @default.
- W4313303885 hasConcept C2777052490 @default.
- W4313303885 hasConcept C33923547 @default.
- W4313303885 hasConcept C37914503 @default.
- W4313303885 hasConcept C41008148 @default.
- W4313303885 hasConcept C41608201 @default.
- W4313303885 hasConcept C62520636 @default.
- W4313303885 hasConcept C82229145 @default.
- W4313303885 hasConcept C9767117 @default.
- W4313303885 hasConcept C99692599 @default.
- W4313303885 hasConceptScore W4313303885C121332964 @default.
- W4313303885 hasConceptScore W4313303885C134306372 @default.
- W4313303885 hasConceptScore W4313303885C154945302 @default.
- W4313303885 hasConceptScore W4313303885C168619227 @default.
- W4313303885 hasConceptScore W4313303885C190470478 @default.
- W4313303885 hasConceptScore W4313303885C202444582 @default.
- W4313303885 hasConceptScore W4313303885C2524010 @default.
- W4313303885 hasConceptScore W4313303885C2777052490 @default.
- W4313303885 hasConceptScore W4313303885C33923547 @default.
- W4313303885 hasConceptScore W4313303885C37914503 @default.
- W4313303885 hasConceptScore W4313303885C41008148 @default.
- W4313303885 hasConceptScore W4313303885C41608201 @default.
- W4313303885 hasConceptScore W4313303885C62520636 @default.
- W4313303885 hasConceptScore W4313303885C82229145 @default.
- W4313303885 hasConceptScore W4313303885C9767117 @default.
- W4313303885 hasConceptScore W4313303885C99692599 @default.
- W4313303885 hasLocation W43133038851 @default.
- W4313303885 hasOpenAccess W4313303885 @default.
- W4313303885 hasPrimaryLocation W43133038851 @default.
- W4313303885 hasRelatedWork W1509570659 @default.
- W4313303885 hasRelatedWork W1976692498 @default.
- W4313303885 hasRelatedWork W1983611176 @default.
- W4313303885 hasRelatedWork W2004165107 @default.
- W4313303885 hasRelatedWork W2077776493 @default.
- W4313303885 hasRelatedWork W2951094680 @default.
- W4313303885 hasRelatedWork W2980231599 @default.
- W4313303885 hasRelatedWork W3043435620 @default.
- W4313303885 hasRelatedWork W4283008489 @default.
- W4313303885 hasRelatedWork W4375959252 @default.
- W4313303885 isParatext "false" @default.
- W4313303885 isRetracted "false" @default.
- W4313303885 workType "article" @default.