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We introduce a special class of real semiflows, which is used to define a general type of evolution semigroups, associated to not necessarily exponentially bounded evolution families. Giving spectral characterizations of the corresponding generators, our results directly apply to a wide class of dichotomies, such as those with time-varying rate of change.

For a discrete dynamics defined by a sequence of bounded and not necessarily invertible linear operators, we give a complete characterization of exponential stability in terms of invertibility of a certain operator acting on suitable Banach sequence spaces. We connect the invertibility of this operator to the existence of a particular type of admissible exponents. For the bounded orbits, exponential stability results from a spectral property. Some adequate examples are presented to emphasize some significant qualitative differences between uniform and nonuniform behavior., Comment: The final version will be published in Journal of Difference Equations and Applications

In this paper we study the infinitesimal symmetries, Newtonoid vector fields, infinitesimal Noether symmetries and conservation laws of Hamiltonian systems. Using the dynamical covariant derivative and Jacobi endomorphism on the cotangent bundle we find the invariant equations of infinitesimal symmetries and Newtonoid vector fields and prove that the canonical nonlinear connection induced by a regular Hamiltonian can be determined by these symmetries. Finally, an example from optimal control theory is given.

For nonuniform exponentially bounded evolution families defined on Banach spaces, we introduce a class of Banach function spaces, whose norms are completely determined by the nonuniform behaviour of the corresponding evolution family. We generalize a classical theorem of Datko on these spaces. In addition, we obtain new criteria for the existence of nonuniform stability.

For nonuniform exponentially bounded evolution families on the half-line we introduce a class of Banach function spaces on which we define nonuniform evolution semigroups. We completely characterize nonuniform exponential stability in terms of invertibility of the corresponding generators. We emphasize that in particular our results apply to all linear differential equations with bounded operator and finite Lyapunov exponent., Comment: 21 pages

In this paper we investigate the relations between semispray, nonlinear connection, dynamical covariant derivative and Jacobi endomorphism on Lie algebroids. Using these geometric structures, we study the symmetries of second order differential equations in the general framework of Lie algebroids., Comment: Section 4 revised, Journal of Geometry and Physics, 2017. arXiv admin note: text overlap with arXiv:1302.5212

In this paper we study the geometrical structures on the cotangent bundle using the notions of adapted tangent structure and regular vector fields. We prove that the dynamical covariant derivative on $T^{*}M$ fix a nonlinear connection for a given $\mathcal{J}$-regular vector field. Using the Legendre transformation induced by a regular Hamiltonian, we show that a semi-Hamiltonian vector field on $T^{*}M$ corresponds to a semispray on $TM$ if and only if the nonlinear connection on $TM$ is just the canonical nonlinear connection induced by the regular Lagrangian., Comment: International Journal of Geometric Methods in Modern Physics, 2016

The paper presents the geometry of Lie algebroids and its applications to optimal control. The first part deals with the theory of Lie algebroids, connections on Lie algebroids and dynamical systems defined on Lie algebroids (mainly Lagrangian and Hamiltonian systems). In the second part we use the framework of Lie algebroids in the study of distributional systems (drift less control affine systems) with holonomic or nonholonomic distributions., Comment: 128 pages

Millions of people are able to exchange information over phones, computers, tablets and an array of new interconnected devices such as sensors, cameras, home appliances and others are increasingly becoming networked. At the core of this sizeable interconnection is a set of underlying protocols that enable millions of devices to seamlessly talk to each other. Aviation, as many other industries have, utilizes the internet protocol for ground-to-ground network communications and efforts are underway to bring it to the cockpit.In 2015, the International Civil Aviation Organization (ICAO) published the second edition of Document 9896 (Doc 9896) titled: Manual on the Aeronautical Telecommunication Network (ATN) using Internet Protocol Suite (IPS) Standards and Protocol. This manual adopted the Internet protocol version 6 (IPv6) for Internet layer interoperability. Document 9896 defined data communications protocols and services to be used for implementing aeronautical telecommunication network (ATN) using the Internet protocol suite (IPS). The document provided technical specifications that addressed security, network and transport protocols, described applications, supported by ATN/IPS and provided communications guidance. The international aviation community working under the guidance of ICAO initiated work on updates to Doc 9896. Under the ICAO Communication Panel, Working Group Internetworking (WG-I) got this challenging task. Key areas of work for WG-I are related to ATN/IPS Security and ANT/IPS Mobility. Two sub-groups have been assembled to work on these elements. The ICAO anticipates the release of updated Doc 9896 in 2020. Additional ATN/IPS standardization efforts include Radio Technical Commission for Aeronautics Special Committee 223 (RTCA SC-223) IPS profile development, Airlines Electronic Engineering Committee (AEEC) A658 Roadmap of IPS future activities and European Organization for Civil Aviation Equipment (EUROCAE) WG-108 development of guidance documentation.This paper describes ICAO WG-I approach to update key areas of the document in closed coordination with AEEC, RTCA and EUROCAE committees supporting the development of ATN/IPS. Additionally, the paper will explore WG-I mobility solutions under investigation, security developments, IPv6 addressing challenges and other proposed updates. Finally, as new operational expectations such as Free Route and Remote Piloted Aircraft System integration are currently pushing the boundaries set by old operational concepts, the paper identifies the emerging new challenges that will drive the ATN/IPS development beyond 2020. They are related to future voice utilization, System Wide Information Management and Remotely Piloted Aircraft System deployment. IPS systems are seen as the only way forward.