Oscillation Numbers for Continuous Lagrangian Paths and Maslov
Index

J 2023

Oscillation Numbers for Continuous Lagrangian Paths and Maslov Index

ELYSEEVA, Julia; Peter ŠEPITKA a Roman ŠIMON HILSCHER

Základní údaje

Originální název

Oscillation Numbers for Continuous Lagrangian Paths and Maslov Index

Autoři

ELYSEEVA, Julia; Peter ŠEPITKA a Roman ŠIMON HILSCHER

Vydání

Journal of Dynamics and Differential Equations, Springer, 2023, 1040-7294

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.400

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/23:00134002

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

Oscillation number; Lagrangian path; Lidskii angle; Symplectic matrix; Comparative index; Maslov index

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 21. 8. 2023 12:36, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

In this paper we present the theory of oscillation numbers and dual oscillation numbers for continuous Lagrangian paths in R-2n. Our main results include a connection of the oscillation numbers of the given Lagrangian path with the Lidskii angles of a special symplectic orthogonal matrix. We also present Sturmian type comparison and separation theorems for the difference of the oscillation numbers of two continuous Lagrangian paths. These results, as well as the definition of the oscillation number itself, are based on the comparative index theory (Elyseeva, 2009). The applications of these results are directed to the theory of Maslov index of two continuous Lagrangian paths. We derive a formula for the Maslov index via the Lidskii angles of a special symplectic orthogonal matrix, and hence we express the Maslov index as the oscillation number of a certain transformed Lagrangian path. The results and methods are based on a generalization of the recently introduced oscillation numbers and dual oscillation numbers for conjoined bases of linear Hamiltonian systems (Elyseeva, 2019 and 2020) and on the connection between the comparative index and Lidskii angles of symplectic matrices (Šepitka and Šimon Hilscher, 2021).

Návaznosti

GA19-01246S, projekt VaV

Název: Nová oscilační teorie pro lineární hamiltonovské a symplektické systémy

Investor: Grantová agentura ČR, Nová oscilační teorie pro lineární hamiltonovské a symplektické systémy

Citovat

ELYSEEVA, Julia; Peter ŠEPITKA a Roman ŠIMON HILSCHER. Oscillation Numbers for Continuous Lagrangian Paths and Maslov Index. Journal of Dynamics and Differential Equations. Springer, 2023, roč. 35, č. 3, s. 2589-2620. ISSN 1040-7294. Dostupné z: https://doi.org/10.1007/s10884-022-10140-7.

@article{1855744,
   author = {Elyseeva, Julia and Šepitka, Peter and Šimon Hilscher, Roman},
   article_number = {3},
   doi = {https://doi.org/10.1007/s10884-022-10140-7},
   keywords = {Oscillation number; Lagrangian path; Lidskii angle; Symplectic matrix; Comparative index; Maslov index},
   language = {eng},
   issn = {1040-7294},
   journal = {Journal of Dynamics and Differential Equations},
   title = {Oscillation Numbers for Continuous Lagrangian Paths and Maslov Index},
   url = {https://link.springer.com/article/10.1007/s10884-022-10140-7},
   volume = {35},
   year = {2023}
}

TY  - JOUR
ID  - 1855744
AU  - Elyseeva, Julia - Šepitka, Peter - Šimon Hilscher, Roman
PY  - 2023
TI  - Oscillation Numbers for Continuous Lagrangian Paths and Maslov Index
JF  - Journal of Dynamics and Differential Equations
VL  - 35
IS  - 3
SP  - 2589-2620
EP  - 2589-2620
PB  - Springer
SN  - 10407294
KW  - Oscillation number
KW  - Lagrangian path
KW  - Lidskii angle
KW  - Symplectic matrix
KW  - Comparative index
KW  - Maslov index
UR  - https://link.springer.com/article/10.1007/s10884-022-10140-7
N2  - In this paper we present the theory of oscillation numbers and dual oscillation numbers for continuous Lagrangian paths in R-2n. Our main results include a connection of the oscillation numbers of the given Lagrangian path with the Lidskii angles of a special symplectic orthogonal matrix. We also present Sturmian type comparison and separation theorems for the difference of the oscillation numbers of two continuous Lagrangian paths. These results, as well as the definition of the oscillation number itself, are based on the comparative index theory (Elyseeva, 2009). The applications of these results are directed to the theory of Maslov index of two continuous Lagrangian paths. We derive a formula for the Maslov index via the Lidskii angles of a special symplectic orthogonal matrix, and hence we express the Maslov index as the oscillation number of a certain transformed Lagrangian path. The results and methods are based on a generalization of the recently introduced oscillation numbers and dual oscillation numbers for conjoined bases of linear Hamiltonian systems (Elyseeva, 2019 and 2020) and on the connection between the comparative index and Lidskii angles of symplectic matrices (Šepitka and Šimon Hilscher, 2021).
ER  -

ELYSEEVA, Julia; Peter ŠEPITKA a Roman ŠIMON HILSCHER. Oscillation Numbers for Continuous Lagrangian Paths and Maslov Index. \textit{Journal of Dynamics and Differential Equations}. Springer, 2023, roč.~35, č.~3, s.~2589-2620. ISSN~1040-7294. Dostupné z: https://doi.org/10.1007/s10884-022-10140-7.

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