Comparative index and Hörmander index in finite dimension and
their connections

J 2023

Comparative index and Hörmander index in finite dimension and their connections

ELYSEEVA, Julia, Peter ŠEPITKA and Roman ŠIMON HILSCHER

Basic information

Original name

Comparative index and Hörmander index in finite dimension and their connections

Authors

ELYSEEVA, Julia, Peter ŠEPITKA (703 Slovakia, belonging to the institution) and Roman ŠIMON HILSCHER (203 Czech Republic, belonging to the institution)

Edition

Filomat, Faculty of Sciences and Mathematics, University of Nis, 2023, 0354-5180

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Serbia

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 0.800 in 2022

RIV identification code

RIV/00216224:14310/23:00134087

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.2298/FIL2316243E

UT WoS

000950895600001

Keywords in English

Comparative index; Maslov index; Hörmander index; Lagrangian plane; Lagrangian path; Triple index; Wronskian

Abstract

V originále

In this paper we prove new relations between the comparative index and the Hörmander index (and the Maslov index) in the finite dimensional case. As a main result we derive an algebraic formula for calculating the Hörmander index of four given Lagrangian planes as a difference of two comparative indices involving certain transformed Lagrangian planes, or as a combination of four comparative indices. This result is based on a generalization of the comparison theorem for the Maslov index involving three Lagrangian paths. In this way we contribute to the recent efforts in the literature (by Zhou, Wu, Zhu in 2018 and by Howard in 2021) devoted to an efficient calculation of the Hörmander index in this finite dimensional case.

Links

GA19-01246S, research and development project

Name: Nová oscilační teorie pro lineární hamiltonovské a symplektické systémy

Investor: Czech Science Foundation

Citovat

ELYSEEVA, Julia, Peter ŠEPITKA and Roman ŠIMON HILSCHER. Comparative index and Hörmander index in finite dimension and their connections. Filomat. Faculty of Sciences and Mathematics, University of Nis, 2023, vol. 37, No 16, p. 5243-5257. ISSN 0354-5180. Available from: https://dx.doi.org/10.2298/FIL2316243E.

@article{2268721,
   author = {Elyseeva, Julia and Šepitka, Peter and Šimon Hilscher, Roman},
   article_number = {16},
   doi = {http://dx.doi.org/10.2298/FIL2316243E},
   keywords = {Comparative index; Maslov index; Hörmander index; Lagrangian plane; Lagrangian path; Triple index; Wronskian},
   language = {eng},
   issn = {0354-5180},
   journal = {Filomat},
   title = {Comparative index and Hörmander index in finite dimension and their connections},
   url = {https://www.pmf.ni.ac.rs/filomat-content/2023/37-16/37-16-6-19561.pdf},
   volume = {37},
   year = {2023}
}

TY  - JOUR
ID  - 2268721
AU  - Elyseeva, Julia - Šepitka, Peter - Šimon Hilscher, Roman
PY  - 2023
TI  - Comparative index and Hörmander index in finite dimension and their connections
JF  - Filomat
VL  - 37
IS  - 16
SP  - 5243-5257
EP  - 5243-5257
PB  - Faculty of Sciences and Mathematics, University of Nis
SN  - 03545180
KW  - Comparative index
KW  - Maslov index
KW  - Hörmander index
KW  - Lagrangian plane
KW  - Lagrangian path
KW  - Triple index
KW  - Wronskian
UR  - https://www.pmf.ni.ac.rs/filomat-content/2023/37-16/37-16-6-19561.pdf
N2  - In this paper we prove new relations between the comparative index and the Hörmander index (and the Maslov index) in the finite dimensional case. As a main result we derive an algebraic formula for calculating the Hörmander index of four given Lagrangian planes as a difference of two comparative indices involving certain transformed Lagrangian planes, or as a combination of four comparative indices. This result is based on a generalization of the comparison theorem for the Maslov index involving three Lagrangian paths. In this way we contribute to the recent efforts in the literature (by Zhou, Wu, Zhu in 2018 and by Howard in 2021) devoted to an efficient calculation of the Hörmander index in this finite dimensional case.
ER  -

ELYSEEVA, Julia, Peter ŠEPITKA and Roman ŠIMON HILSCHER. Comparative index and Hörmander index in finite dimension and their connections. \textit{Filomat}. Faculty of Sciences and Mathematics, University of Nis, 2023, vol.~37, No~16, p.~5243-5257. ISSN~0354-5180. Available from: https://dx.doi.org/10.2298/FIL2316243E.

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