Lyapunov Exponents and Smooth Ergodic Theory
By Luís Barreira, Yakov Pesin. 2002
377 citations recorded by the source corpus.
Subfields: Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a34b0e6790ffd2770ab7cc15980b654b2ec01812
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Control and Systems Engineering
- Adam Czornik
- Michal Niezabitowski
- Dmitry Dolgopyat
- Luís Barreira
- Keith Burns
- Tiago Pereira
- Aneta Stefanovska
- Peter V. E. McClintock
In Mathematical Physics
- Yakov Pesin
- Keith Burns
- Luís Barreira
- F. R. Hertz
- R. Ures
- Mark Pollicott
- Adam Czornik
- Michal Niezabitowski
Citations in the corpus
- Coupling functions:universal insights into dynamical interaction mechanisms (2017, methodology): “The main challenge of the local method lies in the intricacies of the theory of Lyapunov exponents (Barreira and Pesin, 2002; Pikovsky and Politi, 2016).”
- Nonadditive thermodynamic formalism: Equilibrium and Gibbs measures (2006, background): “It follows from Oseledets’ multiplicative ergodic theorem (see for example [ 4 ]), or more precisely from its version for noninvertible transformations, that for each finite f-invariant measure on M there is a set X M of full measure such that if x 2 X then”
- Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows (2005, background): “The monograph by Barreira and Pesin [1] gives a selfcontained treatment of the abstract theory of Lyapunov exponents, which previously was not readily available in English.”
- Stable ergodicity for partially hyperbolic attractors with negative central exponents (2007, methodology): “The measure µ in Theorem 9 and measures µg in Theorems 10 and 11 are SRB measures for f (see [ 2 ] for the definition of SRB measures).”
- New criteria for ergodicity and nonuniform hyperbolicity (2009, background): “For further references, see A. Katok’s paper [23] and the book by L. Barreira and Ya. Pesin [ 10 ].”
- Lyapunov exponents for systems with unbounded coefficients (2013, methodology): “This fact prevents us from using the classical results of the theory of Lyapunov exponents [1] in such cases.”