## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
- Conference Publications
- AIMS Mathematics

DCDS

We generalize the concept of Lyapunov exponent to transformations
that are not necessarily differentiable. For fairly large classes of
repellers and of hyperbolic sets of differentiable maps, the new
exponents are shown to coincide with the classical ones. We also
discuss the relation of the new Lyapunov exponents with the
dimension theory of dynamical systems for invariant sets of
continuous transformations.

DCDS

We give a new definition (different from the one in [14]) for a Lyapunov exponent (called

*new*Lyapunov exponent) associated to a continuous map. Our first result states that these new exponents coincide with the usual Lyapunov exponents if the map is differentiable. Then, we apply this concept to prove that there exists a $C^0$-dense subset of the set of the area-preserving homeomorphisms defined in a compact, connected and boundaryless surface such that any element inside this residual subset has zero*new*Lyapunov exponents for Lebesgue almost every point. Finally, we prove that the function that associates an area-preserving homeomorphism, equipped with the $C^0$-topology, to the integral (with respect to area) of its top*new*Lyapunov exponent over the whole surface cannot be upper-semicontinuous.
DCDS-B

We give necessary integral conditions and sufficient ones for the existence of a general concept of $μ$-dichotomy for evolution operators defined on the half-line which includes as particular cases the well-known concepts of nonuniform exponential dichotomy and nonuniform polynomial dichotomy, and also contains new situations. Additionally, we consider an adapted notion of Lyapunov function and use our results to obtain necessary and sufficient conditions for the existence of nonuniform $μ$-dichotomies using these Lyapunov functions.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]