## 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
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

DCDS

We prove that there is a residual subset $C$, in the space of all $\mathcal C^1$ vector fields
of a closed $n$-manifold $M$, such that for every $X \in \mathcal R$ the set of points in $M$ with Lyapunov
stable $\omega$-limit set is residual in $M$. This improves a result in Arnaud [1] and gives a partial
solution to a conjecture in Hurley [8].

DCDS

We show that diffeomorphisms with a dominated splitting of
the form $E^s\oplus E^c\oplus E^u$, where $E^c$ is a nonhyperbolic
central bundle that splits in a dominated way into
1-dimensional subbundles, are entropy-expansive.
In particular, they have a principal symbolic extension and equilibrium states.

DCDS

We know that two different homoclinic classes contained in the same
hyperbolic set are disjoint [12]. Moreover, a connected
singular-hyperbolic attracting set with dense periodic orbits and a
unique equilibrium is either transitive or the union of two
different homoclinic classes [6]. These results motivate the
questions of if two different homoclinic classes contained in the
same singular-hyperbolic set are disjoint or if the second
alternative in [6] cannot occur. Here we give a negative
answer for both questions. Indeed we prove that every compact
$3$-manifold supports a vector field exhibiting a connected
singular-hyperbolic attracting set which has dense periodic orbits,
a unique singularity, is the union of two homoclinic classes but is
not transitive.

## Year of publication

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