Hamilton extremals in higher order mechanics
Hamiltonian approaches of field theory.
Hamiltonian reduction and quantization on symplectic manifolds.
Hamiltonian stability and subanalytic geometry
In the 70’s, Nekhorochev proved that for an analytic nearly integrable Hamiltonian system, the action variables of the unperturbed Hamiltonian remain nearly constant over an exponentially long time with respect to the size of the perturbation, provided that the unperturbed Hamiltonian satisfies some generic transversality condition known as steepness. Using theorems of real subanalytic geometry, we derive a geometric criterion for steepness: a numerical function which is real analytic around a...
Hamiltonian systems with linear potential and elastic constraints
We consider a class of Hamiltonian systems with linear potential, elastic constraints and arbitrary number of degrees of freedom. We establish sufficient conditions for complete hyperbolicity of the system.
Hamilton-Jacobi theory and moving frames.
Hamilton’s Principle with Variable Order Fractional Derivatives
MSC 2010: 26A33, 70H25, 46F12, 34K37 Dedicated to 80-th birthday of Prof. Rudolf GorenfloWe propose a generalization of Hamilton’s principle in which the minimization is performed with respect to the admissible functions and the order of the derivation. The Euler–Lagrange equations for such minimization are derived. They generalize the classical Euler-Lagrange equation. Also, a new variational problem is formulated in the case when the order of the derivative is defined through a constitutive equation....
Hard and soft sub-time-optimal controllers for a mechanical system with uncertain mass
Hard ball systems are completely hyperbolic.
Hard balls gas and Alexandrov spaces of curvature bounded above.
Helmholtz type condition for mechanical integrators.
Herman’s last geometric theorem
We present a proof of Herman’s Last Geometric Theorem asserting that if is a smooth diffeomorphism of the annulus having the intersection property, then any given -invariant smooth curve on which the rotation number of is Diophantine is accumulated by a positive measure set of smooth invariant curves on which is smoothly conjugated to rotation maps. This implies in particular that a Diophantine elliptic fixed point of an area preserving diffeomorphism of the plane is stable. The remarkable...
Hidden symmetries of the gravitational contact structure of the classical phase space of general relativistic test particle
The phase space of general relativistic test particle is defined as the 1-jet space of motions. A Lorentzian metric defines the canonical contact structure on the odd-dimensional phase space. In the paper we study infinitesimal symmetries of the gravitational contact phase structure which are not generated by spacetime infinitesimal symmetries, i.e. they are hidden symmetries. We prove that Killing multivector fields admit hidden symmetries of the gravitational contact phase structure and we give...
Hierarchy of integrable geodesic flows.
A family of integrable geodesic flows is obtained. Any such a family corresponds to a pair of geodesically equivalent metrics.
High Resolution Tracking of Cell Membrane Dynamics in Moving Cells: an Electrifying Approach
Cell motility is an integral part of a diverse set of biological processes. The quest for mathematical models of cell motility has prompted the development of automated approaches for gathering quantitative data on cell morphology, and the distribution of molecular players involved in cell motility. Here we review recent approaches for quantifying cell motility, including automated cell segmentation and tracking. Secondly, we present our own novel...
Higher symmetries of the Laplacian via quantization
We develop a new approach, based on quantization methods, to study higher symmetries of invariant differential operators. We focus here on conformally invariant powers of the Laplacian over a conformally flat manifold and recover results of Eastwood, Leistner, Gover and Šilhan. In particular, conformally equivariant quantization establishes a correspondence between the algebra of Hamiltonian symmetries of the null geodesic flow and the algebra of higher symmetries of the conformal Laplacian. Combined...
Hill problem analytical theory to the order four: application to the computation of frozen orbits around planetary satellites.
Hofer’s metrics and boundary depth
We show that if is a closed symplectic manifold which admits a nontrivial Hamiltonian vector field all of whose contractible closed orbits are constant, then Hofer’s metric on the group of Hamiltonian diffeomorphisms of has infinite diameter, and indeed admits infinite-dimensional quasi-isometrically embedded normed vector spaces. A similar conclusion applies to Hofer’s metric on various spaces of Lagrangian submanifolds, including those Hamiltonian-isotopic to the diagonal in when satisfies...
Hofer–Zehnder capacity of unit disk cotangent bundles and the loop product
We prove a new finiteness result for the Hofer–Zehnder capacity of certain unit disk cotangent bundles. It is proved by a computation of the pair-of-pants product on Floer homology of cotangent bundles, combined with the theory of spectral invariants. The computation of the pair-of-pants product is reduced to a simple key computation of the Chas–Sullivan loop product.
Homoclinic, Heteroclinic, and Periodic Orbits for a Class of Indefinite Hamiltonian Systems.