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Volume of Singular Hyperbolic Sets
Let X be a C 1+ vector field on a compact Riemannian manifold M with dimension d ≥ 3. Let Λ be a transitive singular hypebolic set with positive...
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Phase Portraits of the Leslie-Gower System
In this paper we characterize the phase portraits of the Leslie-Gower model for competition among species. We give the complete description of their...
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What does a vector field know about volume?
This note provides an affirmative answer to a question of Viterbo concerning the existence of nondiffeomorphic contact forms that share the same.
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Bi-Lyapunov Stable Homoclinic Classes for C1 Generic Flows
We study bi-Lyapunov stable homoclinic classes for a C 1 generic flow on a closed Riemannian manifold and prove that such a homoclinic class contains...
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On Geometry of Vector Fields
It is well known that the study of the geometry and topology of the attainability set of a family of vector fields is one of the main tasks of the...
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A Generalized Lipschitz Shadowing Property for Flows
In this paper, we define a generalized Lipschitz shadowing property for flows and prove that a flow ϕ generated by a C 1 vector field X on a closed...
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Limit Cycle Bifurcations of a Planar Near-Integrable System with Two Small Parameters
In this paper we consider a class of polynomial planar system with two small parameters, ε and λ , satisfying 0 < ε ≪ λ ≪ 1. The corresponding first...
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Recursion Operator in a Noncommutative Minkowski Phase Space
A recursion operator for a geodesic flow, in a noncommutative (NC) phase space endowed with a Minkowski metric, is constructed and discussed in this...
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Hamiltonian Dynamics for the Kepler Problem in a Deformed Phase Space
This work addresses the Hamiltonian dynamics of the Kepler problem in a deformed phase space, by considering the equatorial orbit. The recursion...
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Topaj–Pikovsky Involution in the Hamiltonian Lattice of Locally Coupled Oscillators
We discuss the Hamiltonian model of an oscillator lattice with local coupling. The Hamiltonian model describes localized spatial modes of nonlinear...
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On the notions of singular domination and (multi-)singular hyperbolicity
The properties of uniform hyperbolicity and dominated splitting have been introduced to study the stability of the dynamics of diffeomorphisms. One...
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Exotic Dynamics of Nonholonomic Roller Racer with Periodic Control
In this paper we consider the problem of the motion of the Roller Racer .We assume that the angle ϕ ( t ) between the platforms is a prescribed function...
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Different Models of Rolling for a Robot Ball on a Plane as a Generalization of the Chaplygin Ball Problem
This paper addresses the problem of the rolling of a spherical shell with a frame rotating inside, on which rotors are fastened. It is assumed that...
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On Quasi-weakly Almost Periodic Points of Continuous Flows
Let X be a compact metric space, F : X ×ℝ → X be a continuous flow and x ∈ X a proper quasi-weakly almost periodic point, that is, x is quasi-weakly...
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Comparing Dynamics Initiated by an Attached Oscillating Particle for the Nonholonomic Model of a Chaplygin Sleigh and for a Model with Strong Transverse and Weak Longitudinal Viscous Friction Applied at a Fixed Point on the Body
This paper addresses the problem of a rigid body moving on a plane (a platform) whose motion is initiated by oscillations of a point mass relative to...
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Translating Solitons for the Inverse Mean Curvature Flow
In this paper, we investigate translating solitons for the inverse mean curvature flow (IMCF), which is a special solution deformed only for...
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Regular and Chaotic Dynamics of a Chaplygin Sleigh due to Periodic Switch of the Nonholonomic Constraint
The main goal of the article is to suggest a two-dimensional map that could play the role of a generalized model similar to the standard...
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Darboux polynomials, balances and Painlevé property
For a given polynomial differential system we provide different necessary conditions for the existence of Darboux polynomials using the balances of...
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Extending slow manifold near generic transcritical canard point
We consider the dynamics of planar fast-slow systems near generic transcritical type canard point. By using geometric singular perturbation theory...
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The inertial motion of a roller racer
This paper addresses the problem of the inertial motion of a roller racer , which reduces to investigating a dynamical system on a (two-dimensional)...