Khosro Tajbakhsh

Tarbiat Modares University | TMU · Department of Pure Mathematics

A competitive resource-consumer dynamical model is analyzed based on a novel Lotka-Volterra model similar to Rosenwig-McArthur one. Resource logistic growth in the absence of consumers is logical and widely used by researchers. However, type II Holling's functional response to competing consumers made the model structure more realistic. We used the...

In this paper we show that smooth TA-endomorphisms of compact manifolds with c-expansivity (that is, expansive in the inverse limit) and $C^1$-stable shadowing are Axiom A.

We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and demonstrated that an ITM, endowed with such a measure, is metrically conjugated to an interval exchange map (IEM). This allowed us to extend some properties of IEMs (e.g., an estimate of the...

We study topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduce the maximal invariant measure and demonstrate that an ITM, endowed with such a measure, is metrically conjugated to an interval exchange map (IEM). This allows us to extend some properties of IEMs (e.g. an estimate of the numbe...

In the following text we introduce specification property (stroboscopical property) for dynamical systems on uniform space. We focus on two classes of dynamical systems: generalized shifts and dynamical systems with Alexandroff compactification of a discrete space as phase space. We prove that for a discrete finite topological space X with at least...

In this paper we introduce the notion of "robust special Anosov endomorphisms", and show that Anosov endomorphisms of tori which are not neither an Anosov diffeomorphism nor an expanding map, are not robust special.

In this paper, the acyclic chromatic and the circular list chromatic numbers of a simple H-minor free graph G is considered, where H ∈{K5, K3,3}. It is proved that the acyclic chromatic number (resp. the circular list chromatic number) of a simple H-minor free graph G where H ∈{K5, K3,3} is at most 5 (resp. at most 8) and we conclude that G is star...

In this paper, we investigate the structure of minimum vertex and edge cuts of distance-regular digraphs. We show that each distance-regular digraph Γ, different from an undirected cycle, is super edge-connected, that is, any minimum edge cut of Γ is the set of all edges going into (or coming out of) a single vertex. Moreover, we will show that exc...

We introduce shadowing (specification property, stroboscopical property) for dynamical systems on uniform space. Our focuses on two classes of dynamical systems: generalized shifts and dynamical systems with Alexandroff compactification of a discrete space as phase space. We prove that for a discrete finite topological space $X$ with at least two e...

In this paper we give a classification of special endomorphisms of nil-manifolds: Let $f:N/\Gamma \rightarrow N/\Gamma$ be a covering map of a nil-manifold and denote by $A:N/\Gamma \rightarrow N/\Gamma$ the nil-endomorphism which is homotopic to $f$. If $f$ is a special $TA$-map, then $A$ is a hyperbolic nil-endomorphism and $f$ is topologically c...

For an endomorphism it is known that if all the points in the manifold have dense sets of pre-images then the dynamical system is transitive. But the converse has not been investigated before. Here we are going to show that it is true for Anosov endomorphisms on closed manifolds, by the fact that Anosov endomorphisms are covering maps.

In this paper, we show that the edge connectivity of a distance-regular digraph $\Gamma$ with valency $k$ is $k$ and for $k>2$, any minimum edge cut of $\Gamma$ is the set of all edges going into (or coming out of) a single vertex. Moreover we show that the same result holds for strongly regular digraphs. These results extend the same known results...

In this paper the notion of asymptotic measure expansiveness is introduced and its relationship with dominated splitting is considered. It is proved that if a diffeomorphism admits a co-dimension one dominated splitting then it is asymptotic measure expansive. Also, a diffeomorphism with a homoclinic tangency can be perturbed to a non-asymptotic me...

In this paper we prove that C^1-generically, if a diffeomorphism f on a closed C^{\infty} manifold M satisfies weak specification on a locally maximal set {\Lambda}{\subset}M then {\Lambda} is hyperbolic for f. As a corollary we obtain that C^1-generically, every diffeomorphism with weak specification is Anosov.

In this paper we show that any chain transitive set of a diffeomorphism on a compact C∞-manifold which is C1-stably limit shadowable is hyperbolic. Moreover, it is proved that a locally maximal chain transitive set of a C1-generic diffeomorphism is hyperbolic if and only if it is limit shadowable.

We give a characterization of structurally stable diffeomorphisms by making use of the notion of L p -shadowing property. More precisely, we prove that the set of structurally stable diffeomorphisms coincides with the C 1-interior of the set of diffeomorphisms having L p -shadowing property.

A graph is said to be determined by its adjacency spectrum (or to be a DS graph, for short) if there is no other non-isomorphic graph with the same adjacency spectrum. Although all connected graphs of index less than 2 are known to be determined by their adjacency spectra, the classification of DS graphs of index less than 2 is not complete yet. Th...

Let f be a difieomorphism on a closed manifold M, and let p 2 M be a hyperbolic periodic point of f. Denote Hf(p) the homoclinic class of f associated to p. We say that Hf(p) is C1-stably shadowing if Hf(p) is locally maximal (in U µ M) and there is a C1-neighborhood U(f) of f such that for any g 2 U(f), g has the shadowing property on ⁄g, where ⁄g...

In this paper, we show that if G is a starlike tree, then it is determined by its Laplacian spectrum. Moreover we prove some facts about trees with the same adjacency spectrum as a starlike tree.