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Hyperbolicity and Solvability for Linear Systems on Time Scales. / Крыжевич, Сергей Геннадьевич.

Differential and Difference Equations with Applications. ed. / Peter Kloeden; Sandra Pinelas; Tomas Caraballo; John R. Graef. Vol. 230 Cham : Springer Nature, 2018. p. 221-232 (Springer Proceedings in Mathematics and Statistics; Vol. 230).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

Harvard

Крыжевич, СГ 2018, Hyperbolicity and Solvability for Linear Systems on Time Scales. in P Kloeden, S Pinelas, T Caraballo & JR Graef (eds), Differential and Difference Equations with Applications. vol. 230, Springer Proceedings in Mathematics and Statistics, vol. 230, Springer Nature, Cham, pp. 221-232. https://doi.org/10.1007/978-3-319-75647-9_18

APA

Крыжевич, С. Г. (2018). Hyperbolicity and Solvability for Linear Systems on Time Scales. In P. Kloeden, S. Pinelas, T. Caraballo, & J. R. Graef (Eds.), Differential and Difference Equations with Applications (Vol. 230, pp. 221-232). (Springer Proceedings in Mathematics and Statistics; Vol. 230). Springer Nature. https://doi.org/10.1007/978-3-319-75647-9_18

Vancouver

Крыжевич СГ. Hyperbolicity and Solvability for Linear Systems on Time Scales. In Kloeden P, Pinelas S, Caraballo T, Graef JR, editors, Differential and Difference Equations with Applications. Vol. 230. Cham: Springer Nature. 2018. p. 221-232. (Springer Proceedings in Mathematics and Statistics). https://doi.org/10.1007/978-3-319-75647-9_18

Author

Крыжевич, Сергей Геннадьевич. / Hyperbolicity and Solvability for Linear Systems on Time Scales. Differential and Difference Equations with Applications. editor / Peter Kloeden ; Sandra Pinelas ; Tomas Caraballo ; John R. Graef. Vol. 230 Cham : Springer Nature, 2018. pp. 221-232 (Springer Proceedings in Mathematics and Statistics).

BibTeX

@inproceedings{ebbf871e6e7e43f9ae3be8ca859ef31e,
title = "Hyperbolicity and Solvability for Linear Systems on Time Scales",
abstract = "We believe that the difference between time scale systems and ordinary differential equations is not as big as people use to think. We consider linear operators that correspond to linear dynamic systems on time scales. We study solvability of these operators in L ∞. For ordinary differential equations such solvability is equivalent to hyperbolicity of the considered linear system. Using this approach and transformations of the time variable, we spread the concept of hyperbolicity to time scale dynamics. We provide some analogs of well-known facts of Hyperbolic Systems Theory, e.g. the Lyapunov–Perron theorem on stable manifold. ",
keywords = "Exponential dichotomy, Hyperbolicity, Solvability, Stable manifolds, Time scale",
author = "Крыжевич, {Сергей Геннадьевич}",
note = "Funding Information: The author was partially supported by RFBR grant 18-01-00230-a.",
year = "2018",
month = may,
day = "8",
doi = "10.1007/978-3-319-75647-9_18",
language = "English",
isbn = " 978-3-319-75646-2",
volume = "230",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer Nature",
pages = "221--232",
editor = "Peter Kloeden and Sandra Pinelas and Tomas Caraballo and Graef, {John R.}",
booktitle = "Differential and Difference Equations with Applications",
address = "Germany",

}

RIS

TY - GEN

T1 - Hyperbolicity and Solvability for Linear Systems on Time Scales

AU - Крыжевич, Сергей Геннадьевич

N1 - Funding Information: The author was partially supported by RFBR grant 18-01-00230-a.

PY - 2018/5/8

Y1 - 2018/5/8

N2 - We believe that the difference between time scale systems and ordinary differential equations is not as big as people use to think. We consider linear operators that correspond to linear dynamic systems on time scales. We study solvability of these operators in L ∞. For ordinary differential equations such solvability is equivalent to hyperbolicity of the considered linear system. Using this approach and transformations of the time variable, we spread the concept of hyperbolicity to time scale dynamics. We provide some analogs of well-known facts of Hyperbolic Systems Theory, e.g. the Lyapunov–Perron theorem on stable manifold.

AB - We believe that the difference between time scale systems and ordinary differential equations is not as big as people use to think. We consider linear operators that correspond to linear dynamic systems on time scales. We study solvability of these operators in L ∞. For ordinary differential equations such solvability is equivalent to hyperbolicity of the considered linear system. Using this approach and transformations of the time variable, we spread the concept of hyperbolicity to time scale dynamics. We provide some analogs of well-known facts of Hyperbolic Systems Theory, e.g. the Lyapunov–Perron theorem on stable manifold.

KW - Exponential dichotomy

KW - Hyperbolicity

KW - Solvability

KW - Stable manifolds

KW - Time scale

UR - http://www.scopus.com/inward/record.url?scp=85047184106&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-75647-9_18

DO - 10.1007/978-3-319-75647-9_18

M3 - Conference contribution

SN - 978-3-319-75646-2

VL - 230

T3 - Springer Proceedings in Mathematics and Statistics

SP - 221

EP - 232

BT - Differential and Difference Equations with Applications

A2 - Kloeden, Peter

A2 - Pinelas, Sandra

A2 - Caraballo, Tomas

A2 - Graef, John R.

PB - Springer Nature

CY - Cham

ER -

ID: 26329422